共查询到20条相似文献,搜索用时 15 毫秒
1.
Tengiz Kopaliani George Chelidze 《Journal of Mathematical Analysis and Applications》2009,356(1):232-817
We prove analogies of the classical Gagliardo-Nirenberg inequalities
2.
《Mathematische Nachrichten》2017,290(2-3):187-200
In this paper we consider the k‐plane Nikodym maximal estimates in the variable Lebesgue spaces . We first formulate the problem about the boundedness of the k‐plane Nikodym maximal and show that the maximal estimate in is equivalent to that in for . So, the optimal Nikodym maximal estimate in follows from Cordoba's estimate. 相似文献
3.
Petteri Harjulehto Peter H?st? Yoshihiro Mizuta Tetsu Shimomura 《manuscripta mathematica》2011,135(3-4):381-399
In this paper we study the iterated Hardy?CLittlewood maximal operator in variable exponent Lebesgue spaces with exponent allowed to reach the value 1. We use modulars where the L p(·)-modular is perturbed by a logarithmic-type function, and the results hold also in the more general context of such Musielak?COrlicz spaces. 相似文献
4.
5.
Our aim in this paper is to deal with integrability of maximal functions for generalized Lebesgue spaces with variable exponent. Our exponent approaches 1 on some part of the domain, and hence the integrability depends on the shape of that part and the speed of the exponent approaching 1. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
6.
Alexandre Almeida Humberto Rafeiro 《Journal of Mathematical Analysis and Applications》2008,340(2):1336-1346
We study the inversion problem of the Bessel potential operator within the frameworks of the weighted Lebesgue spaces with variable exponent. The inverse operator is constructed by using approximative inverse operators. This generalizes some classical results to the variable exponent setting. 相似文献
7.
Aleš Nekvinda 《Journal of Mathematical Analysis and Applications》2008,337(2):1345-1365
We study general Lebesgue spaces with variable exponent p. It is known that the classes L and N of functions p are such that the Hardy-Littlewood maximal operator is bounded on them provided p∈L∩P. The class L governs local properties of p and N governs the behavior of p at infinity.In this paper we focus on the properties of p near infinity. We extend the class N to a collection D of functions p such that the Hardy-Littlewood maximal operator is bounded on the corresponding variable Lebesgue spaces provided p∈L∩D and the class D is essentially larger than N.Moreover, the condition p∈D is quite easily verifiable in the practice. 相似文献
8.
A. Fiorenza A. Gogatishvili T. Kopaliani 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2014,49(5):232-240
In this paper we study some estimates of norms in variable exponent Lebesgue spaces for singular integral operators that are imaginary powers of the Laplace operator in ? n . Using the Mellin transform argument, fromthese estimates we obtain the boundedness for a family of maximal operators in variable exponent Lebesgue spaces, which are closely related to the (weak) solution of the wave equation. 相似文献
9.
Let \({M_\beta }\) be the fractional maximal function. The commutator generated by \({M_\beta }\) and a suitable function b is defined by \([{M_\beta },b]f = {M_\beta }(bf) - b{M_\beta }(f)\) . Denote by P(? n ) the set of all measurable functions p(·): ? n → [1,∞) such that $1 < p_ - : = \mathop {es\sin fp(x)}\limits_{x \in \mathbb{R}^n } andp_ + : = \mathop {es\operatorname{s} \sup p(x) < \infty }\limits_{x \in \mathbb{R}^n } ,$ and by B(? n ) the set of all p(·) ∈ P(? n ) such that the Hardy-Littlewood maximal function M is bounded on L p(·)(? n ). In this paper, the authors give some characterizations of b for which \([{M_\beta },b]\) is bounded from L p(·)(? n ) into L q(·)(? n ), when p(·) ∈ P(? n ), 0 < β < n/p + and 1/q(·) = 1/p(·) ? β/n with q(·)(n ? β)/n ∈ B(? n ). 相似文献
10.
Rovshan A. Bandaliev 《Czechoslovak Mathematical Journal》2010,60(2):327-337
The main purpose of this paper is to prove the boundedness of the multidimensional Hardy type operator in weighted Lebesgue
spaces with a variable exponent. As an application we prove the boundedness of certain sublinear operators on the weighted
variable Lebesgue space. 相似文献
11.
We study two-weight inequalities with general-type weights for Hardy-Littlewood maximal operator in the Lebesgue spaces with
variable exponent. The exponent function satisfies log-Holder-type local continuity condition and decay condition in infinity.
The right-hand side weight to the certain power satisfies the doubling condition. Sawyer-type two-weight criteria for fractional
maximal functions are derived. 相似文献
12.
For and variable exponents and with values in [1, ∞], let the variable exponents be defined by The Riesz–Thorin–type interpolation theorem for variable Lebesgue spaces says that if a linear operator T acts boundedly from the variable Lebesgue space to the variable Lebesgue space for , then where C is an interpolation constant independent of T. We consider two different modulars and generating variable Lebesgue spaces and give upper estimates for the corresponding interpolation constants Cmax and Csum, which imply that and , as well as, lead to sufficient conditions for and . We also construct an example showing that, in many cases, our upper estimates are sharp and the interpolation constant is greater than one, even if one requires that , are Lipschitz continuous and bounded away from one and infinity (in this case, ). 相似文献
13.
We compute the right and left democracy functions of admissible wavelet bases in variable Lebesgue spaces defined on \(\mathbb R^n\). As an application we give Lebesgue type inequalities for these wavelet bases. We also show that our techniques can be easily modified to prove analogous results for weighted variable Lebesgue spaces and variable exponent Triebel–Lizorkin spaces. 相似文献
14.
Przemysław Górka 《Periodica Mathematica Hungarica》2016,72(2):243-247
We prove an Ergodic Theorem in variable exponent Lebesgue spaces, whenever the exponent is invariant under the transformation. Moreover, a counterexample is provided which shows that the norm convergence fails to hold for an arbitrary exponent. 相似文献
15.
Tengiz Kopaliani 《Journal of Functional Analysis》2009,257(11):3541-3551
When Hardy-Littlewood maximal operator is bounded on Lp(⋅)(Rn) space we prove θ[Lp(⋅)(Rn),BMO(Rn)]=Lq(⋅)(Rn) where q(⋅)=p(⋅)/(1−θ) and θ[Lp(⋅)(Rn),H1(Rn)]=Lq(⋅)(Rn) where 1/q(⋅)=θ+(1−θ)/p(⋅). 相似文献
16.
The family of block spaces with variable exponents is introduced. We obtain some fundamental properties of the family of block spaces with variable exponents. They are Banach lattices and they are generalizations of the Lebesgue spaces with variable exponents. Moreover, the block space with variable exponents is a pre-dual of the corresponding Morrey space with variable exponents. The main result of this paper is on the boundedness of the Hardy-Littlewood maximal operator on the block space with variable exponents. We find that the Hardy-Littlewood maximal operator is bounded on the block space with variable exponents whenever the Hardy-Littlewood maximal operator is bounded on the corresponding Lebesgue space with variable exponents. 相似文献
17.
In this note, we study boundedness of a large class of maximal operators in Sobolev spaces that includes the spherical maximal operator. We also study the size of the set of Lebesgue points with respect to convergence associated with such maximal operators. 相似文献
18.
Boundedness of maximal operators and potential operators on Carleson curves in Lebesgue spaces with variable exponent 总被引:1,自引:0,他引:1
We prove the boundedness of the maximal operator Mr in the spaces L^p(·)(Г,p) with variable exponent p(t) and power weight p on an arbitrary Carleson curve under the assumption that p(t) satisfies the log-condition on Г. We prove also weighted Sobolev type L^p(·)(Г, p) → L^q(·)(Г, p)-theorem for potential operators on Carleson curves. 相似文献
19.
Hitoshi Tanaka 《Proceedings of the American Mathematical Society》2001,129(8):2373-2378
Let , , be the Kakeya maximal operator defined as the supremum of averages over tubes of the eccentricity . We shall prove the so-called Fefferman-Stein type inequality for ,
in the range , , with some constants and independent of and the weight .