共查询到20条相似文献,搜索用时 562 毫秒
1.
A Shilla graph is defined as a distance-regular graph of diameter 3 with second eigen-value θ1 equal to a3. For a Shilla graph, let us put a = a3 and b = k/a. It is proved in this paper that a Shilla graph with b2 = c2 and noninteger eigenvalues has the following intersection array: If Γ is a Q-polynomial Shilla graph with b2 = c2 and b = 2r, then the graph Γ has intersection array and, for any vertex u in Γ, the subgraph Γ3(u) is an antipodal distance-regular graph with intersection array The Shilla graphs with b2 = c2 and b = 4 are also classified in the paper.
相似文献
$$\left\{ {\frac{{{b^2}\left( {b - 1} \right)}}{2},\frac{{\left( {b - 1} \right)\left( {{b^2} - b + 2} \right)}}{2},\frac{{b\left( {b - 1} \right)}}{4};1,\frac{{b\left( {b - 1} \right)}}{4},\frac{{b{{\left( {b - 1} \right)}^2}}}{2}} \right\}$$
$$\left\{ {2tr\left( {2r + 1} \right),\left( {2r + 1} \right)\left( {2rt + t + 1} \right),r\left( {r + t} \right);1,r\left( {r + t} \right),t\left( {4{r^2} - 1} \right)} \right\}$$
$$\left\{ {t\left( {2r + 1} \right),\left( {2r - 1} \right)\left( {t + 1} \right),1;1,t + 1,t\left( {2r + 1} \right)} \right\}$$
2.
In this paper, we consider the logarithmically improved regularity criterion for the supercritical quasi-geostrophic equation in Besov space \(\dot B_{\infty ,\infty }^{ - r}\left( {{\mathbb{R}^2}} \right)\). The result shows that if θ is a weak solutions satisfies then θ is regular at t = T. In view of the embedding \({L^{\frac{2}{r}}} \subset M_{\frac{2}{r}}^p \subset \dot B_{\infty ,\infty }^{ - r}\) with \(2 \leqslant p < \frac{2}{r}\) and 0 ≤ r < 1, we see that our result extends the results due to [20] and [31].
相似文献
$$\int_0^T {\frac{{\left\| {\nabla \theta ( \cdot ,s)} \right\|_{\dot B_{\infty ,\infty }^{ - r} }^{\tfrac{\alpha }{{\alpha - r}}} }}{{1 + \ln \left( {e + \left\| {\nabla ^ \bot \theta ( \cdot ,s)} \right\|_{L^{\tfrac{2}{r}} } } \right)!}}ds < \infty for some 0 < r < \alpha and 0 < \alpha < 1,}$$
3.
Jay Taylor 《Israel Journal of Mathematics》2017,217(1):435-475
In this paper we establish the following estimate: where ω ≥ 0, 0 < ε < 1 and Φ(t) = t(1 + log+(t)). This inequality relies upon the following sharp L p estimate: where 1 < p < ∞, ω ≥ 0 and 0 < δ < 1. As a consequence we recover the following estimate essentially contained in [18]: We also obtain the analogue estimates for symbol-multilinear commutators for a wider class of symbols.
相似文献
$$\omega \left( {\left\{ {x \in {\mathbb{R}^n}:\left| {\left[ {b,T} \right]f\left( x \right)} \right| > \lambda } \right\}} \right) \leqslant \frac{{{c_T}}}{{{\varepsilon ^2}}}\int_{{\mathbb{R}^n}} {\Phi \left( {{{\left\| b \right\|}_{BMO}}\frac{{\left| {f\left( x \right)} \right|}}{\lambda }} \right){M_{L{{\left( {\log L} \right)}^{1 + \varepsilon }}}}} \omega \left( x \right)dx$$
$${\left\| {\left[ {b,T} \right]f} \right\|_{{L^p}\left( \omega \right)}} \leqslant {c_T}{\left( {p'} \right)^2}{p^2}{\left( {\frac{{p - 1}}{\delta }} \right)^{\frac{1}{{p'}}}}{\left\| b \right\|_{BMO}}{\left\| f \right\|_{{L^p}\left( {{M_{L{{\left( {{{\log }_L}} \right)}^{2p - 1 + {\delta ^\omega }}}}}} \right)}}$$
$$\omega \left( {\left\{ {x \in {\mathbb{R}^n}:\left| {\left[ {b,T} \right]f\left( x \right)} \right| > \lambda } \right\}} \right) \leqslant {c_T}{\left[ \omega \right]_{{A_\infty }}}{\left( {1 + {{\log }^ + }{{\left[ \omega \right]}_{{A_\infty }}}} \right)^2}\int_{{\mathbb{R}^n}} {\Phi \left( {{{\left\| b \right\|}_{BMO}}\frac{{\left| {f\left( x \right)} \right|}}{\lambda }} \right)M} \omega \left( x \right)dx.$$
4.
A remark on the existence of entire large and bounded solutions to a (<Emphasis Type="Italic">k</Emphasis><Subscript>1</Subscript>, <Emphasis Type="Italic">k</Emphasis><Subscript>2</Subscript>)-Hessian system with gradient term
下载免费PDF全文
![点击此处可从《数学学报(英文版)》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Dragos Patru Covei 《数学学报(英文版)》2017,33(6):761-774
In this paper, we study the existence of positive entire large and bounded radial positive solutions for the following nonlinear system Here \({S_{{k_i}}}\left( {\lambda \left( {{D^2}{u_i}} \right)} \right)\) is the k i -Hessian operator, a 1, p 1, f 1, a 2, p 2 and f 2 are continuous functions.
相似文献
$$\left\{ {\begin{array}{*{20}c}{S_{k_1 } \left( {\lambda \left( {D^2 u_1 } \right)} \right) + a_1 \left( {\left| x \right|} \right)\left| {\nabla u_1 } \right|^{k_1 } = p_1 \left( {\left| x \right|} \right)f_1 \left( {u_2 } \right)} & {for x \in \mathbb{R}^N ,} \\{S_{k_2 } \left( {\lambda \left( {D^2 u_2 } \right)} \right) + a_2 \left( {\left| x \right|} \right)\left| {\nabla u_2 } \right|^{k_2 } = p_2 \left( {\left| x \right|} \right)f_2 \left( {u_1 } \right)} & {for x \in \mathbb{R}^N .} \\\end{array} } \right.$$
5.
In this paper, we consider the two-dimensional Hausdorff operators on the power weighted Hardy space H_(|x|α)~1(R~2) ( -1 ≤α≤0), defined by H_(Φ,A)f(x)=∫R~2Φ(u)f(A(u)x)du,where Φ∈L_loc~1(R~2),A(u) = (α_(ij)(u))_(i,j=1)~2 is a 2×2 matrix, and each α_(i,j) is a measurablefunction.We obtain that HΦ,A is bounded from H_(|x|~α)~1(R~2) ( -1≤α≤0) to itself, if∫R2|Φ(u)‖det A~(-1)(u)|‖A(u)‖~(-α)ln(1+‖A~(-1)(u)‖~2/|det A~(-1)(u)|)du∞.This result improves some known theorems, and in some sense it is sharp. 相似文献
6.
In this note we consider Wente's type inequality on the Lorentz-Sobolev space.If▽f∈L~p1,q1(R~n),G ∈ L~(p2,q2)(R~n) and div G≡0 in the sense of distribution where(1/p1)+(1/P2)=(1/q1)+(1/q2)=1,1P1,P2∞,it is known that G·▽f belongs to the Hardy space H~1 and furthermore‖G·▽f‖H~1≤C‖▽f‖L~(p1,q1)(R~2)‖G‖L~(p2,q2)(R~2).Reader can see[9]Section 4.Here we give a new proof of this result.Our proof depends on an estimate of a maximal operator on the Lorentz space which is of some independent interest.Finally,we use this inequality to get a generalisation of Bethuel's inequality. 相似文献
7.
Pavel Trojovský 《P-Adic Numbers, Ultrametric Analysis, and Applications》2017,9(3):228-235
Let (F n ) n≥0 be the Fibonacci sequence. For 1 ≤ k ≤ m, the Fibonomial coefficient is defined as . In 2013, Marques, Sellers and Trojovský proved that if p is a prime number such that p ≡ ±2 (mod 5), then \(p{\left| {\left[ {\begin{array}{*{20}{c}} {{p^{a + 1}}} \\ {{p^a}} \end{array}} \right]} \right._F}\) for all integers a ≥ 1. In 2015, Marques and Trojovský worked on the p-adic order of \({\left[ {\begin{array}{*{20}{c}} {{p^{a + 1}}} \\ {{p^a}} \end{array}} \right]_F}\) for all a ≥ 1 when p ≠ 5. In this paper, we shall provide the exact p-adic order of \({\left[ {\begin{array}{*{20}{c}} {{p^{a + 1}}} \\ {{p^a}} \end{array}} \right]_F}\) for all integers a, b ≥ 1 and for all prime number p.
相似文献
$${\left[ {\begin{array}{*{20}{c}} m \\ k \end{array}} \right]_F} = \frac{{{F_{m - k + 1}} \cdots {F_{m - 1}}{F_m}}}{{{F_1} \cdots {F_k}}}$$
8.
S. Gulzar 《Analysis Mathematica》2016,42(4):339-352
For a polynomial P(z) of degree n having no zeros in |z| < 1, it was recently proved in [9] that for every β ∈ C with |β| ≤ 1, 1 ≤ s ≤ n and |z| = 1. In this paper, we obtain the L p mean extension of the above and other related results for the sth derivative of polynomials.
相似文献
$$\left| {{z^s}{P^{\left( s \right)}}\left( z \right) + \beta \frac{{n\left( {n - 1} \right)...\left( {n - s + 1} \right)}}{{{2^s}}}P\left( z \right)} \right| \leqslant \frac{{n\left( {n - 1} \right)...\left( {n - s + 1} \right)}}{2}\left( {\left| {1 + \frac{\beta }{{{2^s}}}} \right| + \left| {\frac{\beta }{{{2^s}}}} \right|} \right)\mathop {\max }\limits_{\left| z \right| = 1} \left| {P\left( z \right)} \right|$$
9.
10.
Following an idea of Lin, we prove that if A and B are two positive operators such that 0 mI ≤ A ≤m'I≤ M'I ≤ B ≤ MI, then Φ~2(A+B/2)≤K~2(h)/(1+(logM'/m'/g))~2Φ~2(A≠B) and Φ~2(A+B/2)≤K~2(h)/(1+(logM'/m'/g))~2(Φ(A)≠Φ(B))~2 where K(h)=(h+1)~2/4 and h = M/m and Φ is a positive unital linear map. 相似文献
11.
Hrmander Type Theorem for Fourier Multipliers with Optimal Smoothness on Hardy Spaces of Arbitrary Number of Parameters
下载免费PDF全文
![点击此处可从《数学学报(英文版)》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Jiao Chen 《数学学报(英文版)》2017,33(8):1083-1106
The main purpose of this paper is to establish the Hormander-Mihlin type theorem for Fourier multipliers with optimal smoothness on k-parameter Hardy spaces for k≥ 3 using the multiparameter Littlewood-Paley theory. For the sake of convenience and simplicity, we only consider the case k = 3, and the method works for all the cases k≥ 3:■where x =(x_1,x_2,x_3)∈R~(n_1)×R~(n_2)×R~(n_3) and ξ =(ξ_1,ξ_2,ξ_3)∈R~(n_1)×R~(n_2)×R~(n_3). One of our main results is the following:Assume that m(ξ) is a function on R~(n_1+n_2+n_3) satisfying ■ with s_i n_i(1/p-1/2) for 1≤i≤3. Then T_m is bounded from H~p(R~(n_1)×R~(n_2)×R~(n_3) to H~p(R~(n_1)×R~(n_2)×R~(n_3)for all 0 p≤1 and ■ Moreover, the smoothness assumption on s_i for 1≤i≤3 is optimal. Here we have used the notations m_(j,k,l)(ξ)=m(2~jξ_1,2~kξ_2,2~lξ_3)Ψ(ξ_1)Ψ(ξ_2)Ψ(ξ_3) and Ψ(ξ_i) is a suitable cut-off function on R~(n_i) for1≤i≤3, and W~(s_1,s_2,s_3) is a three-parameter Sobolev space on R~(n_1)×R~(n_2)× R~(n_3).Because the Fefferman criterion breaks down in three parameters or more, we consider the L~p boundedness of the Littlewood-Paley square function of T_mf to establish its boundedness on the multi-parameter Hardy spaces. 相似文献
12.
Natalia Budarina 《Lithuanian Mathematical Journal》2011,51(4):461-471
In this paper, we show that if the volume sum \( \sum\nolimits_{h = 1}^\infty {{h^{n - 1}}{\Psi^t}(h)} \) converges for a function ψ (not necessarily monotonic), then the set of points \( \left( {x,{w_1}, \ldots, {w_{t - 1}}} \right) \in {\mathbb R} \times {{\mathbb Q}_{{p_1}}} \times \ldots \times {{\mathbb Q}_{{p_{t - 1}}}} \) that simultaneously satisfy the inequalities \( \left| {P(x)} \right| < \Psi (H) {\text{and}} {\left| {P\left( {{w_i}} \right)} \right|_{{p_i}}} < \Phi (H), 1 \leqslant i \leqslant t - 1 \), for infinitely many integer polynomials P has measure zero. 相似文献
13.
Let M Ω be the maximal operator with homogeneous kernel Ω. In the present paper, we show that if Ω satisfies the L 1-Dini condition on ?? n?1, then the following weak type (1,1) behaviors
hold for the maximal operator M Ω and \(f\in L^{1}(\mathbb {R}^{n})\), here \(\tilde {\omega }_{1}\) denotes the L 1 integral modulus of continuity of Ω defined by translation in \(\mathbb {R}^{n}\). 相似文献
$$\lim\limits _{\lambda \rightarrow 0_{+}}\lambda m(\{x\in \mathbb {R}^{n}:M_{\Omega } f(x)>\lambda \})=\frac {1}{n} \|\Omega \|_{1} \|f\|_{1},$$
$$\sup\limits_{\lambda >0}\lambda m(\{x\in \mathbb {R}^{n}:M_{\Omega } f(x)>\lambda \})\lesssim {\bigg ((\log n)\|\Omega \|_{1}+{\int }_{0}^{1/n}\frac {\tilde {\omega }_{1}(\delta )}{\delta }d\delta \bigg )}\|f\|_{1}$$
14.
S. B. Gashkov 《Mathematical Notes》2016,100(5-6):666-676
For the linear positive Korovkin operator \(f\left( x \right) \to {t_n}\left( {f;x} \right) = \frac{1}{\pi }\int_{ - \pi }^\pi {f\left( {x + t} \right)E\left( t \right)dt} \), where E(x) is the Egervary–Szász polynomial and the corresponding interpolation mean \({t_{n,N}}\left( {f;x} \right) = \frac{1}{N}\sum\limits_{k = - N}^{N - 1} {{E_n}\left( {x - \frac{{\pi k}}{N}} \right)f\left( {\frac{{\pi k}}{N}} \right)} \), the Jackson-type inequalities \(\left\| {{t_{n,N}}\left( {f;x} \right) - f\left( x \right)} \right\| \leqslant \left( {1 + \pi } \right){\omega _f}\left( {\frac{1}{n}} \right),\left\| {{t_{n,N}}\left( {f;x} \right) - f\left( x \right)} \right\| \leqslant 2{\omega _f}\left( {\frac{\pi }{{n + 1}}} \right)\), where ωf (x) denotes the modulus of continuity, are proved for N > n/2. For ωf (x) ≤ Mx, the inequality \(\left\| {{t_{n,N}}\left( {f;x} \right) - f\left( x \right)} \right\| \leqslant \frac{{\pi M}}{{n + 1}}\). is established. As a consequence, an elementary derivation of an asymptotically sharp estimate of the Kolmogorov width of a compact set of functions satisfying the Lipschitz condition is obtained. 相似文献
15.
We calculate the sharp bounds for some q-analysis variants of Hausdorff type inequalities of the form . As applications, we obtain several sharp q-analysis inequalities of the classical positive integral operators, including the Hardy operator and its adjoint operator, the Hilbert operator, and the Hardy-Littlewood-Pólya operator.
相似文献
$$\int_0^{ + \infty } {{{\left( {\int_0^{ + \infty } {\frac{{\phi \left( t \right)}}{t}f\left( {\frac{x}{t}} \right){d_q}t} } \right)}^p}{d_q}x} \leqslant {C_\phi }\int_0^b {{f^p}\left( t \right)} {d_q}t$$
16.
B. F. Ivanov 《Vestnik St. Petersburg University: Mathematics》2017,50(4):354-363
Suppose that m ≥ 2, numbers p 1, …, p m ∈ (1, +∞] satisfy the inequality \(\frac{1}{{{p_1}}} + \cdots + \frac{1}{{{p_m}}} < 1\), and functions \({\gamma _1} \in {L^{{p_1}}}\left( {{?^1}} \right), \cdots ,{\gamma _m} \in {L^{{p_m}}}\left( {{?^1}} \right)\) are given. It is proved that if the set of “resonance” points of each of these functions is nonempty and the “nonresonance” condition holds (both notions were defined by the author for functions in L p (?1), p ∈ (1, +∞]), then \(\mathop {\sup }\limits_{a,b \in {R^1}} \left| {\mathop \smallint \limits_a^b \prod\limits_{k = 1}^m {[{\gamma _k}\left( \tau \right) + \Delta {\gamma _k}\left( \tau \right)]} d\tau } \right| \leqslant C\prod\limits_{k = 1}^m {{{\left\| {{\gamma _k} + \Delta {\gamma _k}} \right\|}_{L_{ak}^{pk}\left( {{R^1}} \right)}}} \) where the constant C > 0 is independent of the functions \(\Delta {\gamma _k} \in L_{ak}^{pk}\left( {{?^1}} \right)\) and \(L_{ak}^{pk}\left( {{?^1}} \right) \subset {L^{pk}}\left( {{?^1}} \right)\), 1 ≤ k ≤ m, are special normed spaces. A condition for the integral over ?1 of a product of functions to be bounded is also given. 相似文献
17.
Let {X n }n?≥?1 be a sequence of strictly stationary m-dependent random variableswith EX1 = 0 and \( \mathrm{E}{X}_1^2<\infty \), and let (b n ) be an increasing sequence of positive numbers such that b n ?↑?∞ and \( {b}_n/\sqrt{n}\downarrow 0\kern0.5em \mathrm{as}\kern0.5em n\to \infty \). We establish a moderate deviation principle of \( {\left({b}_n\sqrt{n}\right)}^{-1}{\sum}_{i=1}^n{X}_i \) under the condition
which is weaker than the classical exponential integrability condition. The results in the present paper weaken the assumptions of Chen [5] and extend partially the results of Eichelsbacher and Löwe [10]. 相似文献
$$ \underset{n\to \infty }{\lim \sup}\frac{1}{b_n^2}\log \left[n\mathbf{P}\left(\left|{X}_1\right|>{b}_n\sqrt{n}\right)\right]=-\infty, $$
18.
B. F. Ivanov 《Vestnik St. Petersburg University: Mathematics》2017,50(3):265-273
Let m ≥ 2, the numbers p 1,…, p m ∈ (1, +∞] satisfy the inequality \(\frac{1}{{{p_1}}} + ...\frac{1}{{{p_m}}} < 1\), and γ1 ∈ L p1(?1), …, γ m ∈ \({L^{{p_m}}}\)(?1). We prove that, if the set of “resonance” points of each of these functions is nonempty and the “nonresonance” condition holds (both concepts have been introduced by the author for functions of spaces L p (?1), p ∈ (1, +∞]), we have the inequality \(\mathop {\sup }\limits_{a,b \in {R^1}} \left| {\int\limits_a^b {\prod\limits_{k = 1}^m {\left[ {{\gamma _k}\left( \tau \right) + \Delta {\gamma _k}\left( \tau \right)} \right]} d\tau } } \right| \leqslant C{\prod\limits_{k = 1}^m {\left\| {{\gamma _k} + \Delta {\gamma _k}} \right\|} _{L_{{a_k}}^{{p_k}}}}\left( {{\mathbb{R}^1}} \right)\), where the constant C > 0 is independent of functions \(\Delta {\gamma _k} \in L_{{a_k}}^{{p_k}}\left( {{\mathbb{R}^1}} \right)\) and \(L_{{a_k}}^{{p_k}}\left( {{\mathbb{R}^1}} \right) \subset {L^{{p_k}}}\left( {{\mathbb{R}^1}} \right)\), 1 ≤ k ≤ m are some specially constructed normed spaces. In addition, we give a boundedness condition for the integral of the product of functions over a subset of ?1. 相似文献
19.
Let n ≥ 2 and let Ω ? ? n be an open set. We prove the boundedness of weak solutions to the problem where ? is a Young function such that the space W 0 1 L Φ(Ω) is embedded into an exponential or multiple exponential Orlicz space, the nonlinearity f(x, t) has the corresponding critical growth, V(x) is a continuous potential, h ∈ L Φ(Ω) is a non-trivial continuous function and µ ≥ 0 is a small parameter. We consider two classical cases: the case of Ω being an open bounded set and the case of Ω = ? n .
相似文献
$$u \in W_0^1 L^\Phi \left( \Omega \right) and - div\left( {\Phi '\left( {\left| {\nabla u} \right|} \right)\frac{{\nabla u}}{{\left| {\nabla u} \right|}}} \right) + V\left( x \right)\Phi '\left( {\left| u \right|} \right)\frac{u}{{\left| u \right|}} = f\left( {x,u} \right) + \mu h\left( x \right) in \Omega ,$$
20.
Using measure-capacity inequalities we study new functional inequalities, namely L
q
-Poincaré inequalities
and L
q
-logarithmic Sobolev inequalities
for any q ∈ (0, 1]. As a consequence, we establish the asymptotic behavior of the solutions to the so-called weighted porous media
equation
for m ≥ 1, in terms of L
2-norms and entropies.
相似文献