共查询到20条相似文献,搜索用时 750 毫秒
1.
Jorge J. Betancor Juan C. Fariña Lourdes Rodríguez-Mesa Ricardo Testoni José Luis Torrea 《Journal of Mathematical Analysis and Applications》2012,386(2):487-504
Carlos Segovia and Richard Wheeden defined fractional square functions involving fractional derivatives. They obtained characterizations of potential spaces via square functions. Our aim in this paper is to reconsider the ideas of Segovia and Wheeden under the light of the semigroups of operators. We develop a quite general theory of fractional square functions associated to certain classes of operators. We present some examples of differential operators where our theory applies. We recover in a more compact way the results of Segovia and Wheeden and we obtain new characterizations of the potential spaces associated to the harmonic oscillator and Ornstein–Uhlenbeck operators. 相似文献
2.
We obtain (essentially sharp) boundedness results for certain generalized local maximal operators between fractional weighted Sobolev spaces and their modifications. Concrete boundedness results between well known fractional Sobolev spaces are derived as consequences of our main result. We also apply our boundedness results by studying both generalized neighbourhood capacities and the Lebesgue differentiation of fractional weighted Sobolev functions. 相似文献
3.
Weighted Weak-type Estimates for Multilinear Commutators of Fractional Integrals on Spaces of Homogeneous Type 总被引:5,自引:1,他引:4
Osvaldo GOROSITO Gladis PRADOLINI Oscar SALINAS 《数学学报(英文版)》2007,23(10):1813-1826
We obtain weighted distributional inequalities for multilinear commutators of the fractional integral on spaces of homogeneous type, The techniques developed in this work involve the behavior of some fractional maximal functions. In relation to these operators, as a main tool, we prove a weighted weak type boundedness result, which is interesting in itself. 相似文献
4.
5.
In this paper, we study several radial basis function approximation schemes in Sobolev spaces. We obtain an optional error estimate by using a class of smoothing operators. We also discussed sufficient conditions for the smoothing operators to attain the desired approximation order. We then construct the smoothing operators by some compactly supported radial kernels, and use them to approximate Sobolev space functions with optimal convergence order. These kernels can be simply constructed and readily applied to practical problems. The results show that the approximation power depends on the precision of the sampling instrument and the density of the available data. 相似文献
6.
7.
Kangqun Zhang 《Mathematical Methods in the Applied Sciences》2020,43(6):2845-2857
By studying a weakly singular integral whose kernel involves Mittag-Leffler functions, we obtain some new Gronwall-type integral inequalities. Applying these inequalities and fixed point theorems, existence and uniqueness of positive solution of initial value problem to nonlinear fractional differential equation with Caputo-like counterpart hyper-Bessel operators are established. 相似文献
8.
We obtain new convolutions for quadratic-phase Fourier integral operators (which include, as subcases, e.g., the fractional Fourier transform and the linear canonical transform). The structure of these convolutions is based on properties of the mentioned integral operators and takes profit of weight-functions associated with some amplitude and Gaussian functions. Therefore, the fundamental properties of that quadratic-phase Fourier integral operators are also studied (including a Riemann–Lebesgue type lemma, invertibility results, a Plancherel type theorem and a Parseval type identity). As applications, we obtain new Young type inequalities, the asymptotic behaviour of some oscillatory integrals, and the solvability of convolution integral equations. 相似文献
9.
Bruno Franchi Carlos Pérez Richard L. Wheeden 《Journal of Fourier Analysis and Applications》2003,9(5):511-540
We define a class of summation operators with applications to the self-improving
nature of Poincaré–Sobolev estimates, in fairly general quasimetric spaces of homogeneous type.
We show that these sum operators play the familiar role of integral operators of potential type (e.g.,
Riesz fractional integrals) in deriving Poincaré–Sobolev estimates in cases when representations
of functions by such integral operators are not readily available. In particular, we derive norm
estimates for sum operators and use these estimates to obtain improved Poincaré–Sobolev results. 相似文献
10.
Yueshan Wang 《分析论及其应用》2017,33(2)
Considering a class of operators which include fractional integrals related to operators with Gaussian kernel bounds,the fractional integral operators with rough kernels and fractional maximal operators with rough kernels as special cases,we prove that if these operators are bounded on weighted Lebesgue spaces and satisfy some local pointwise control,then these operators and the commutators of these operators with a BMO functions are also bounded on generalized weighted Morrey spaces. 相似文献
11.
Since the spherical Gaussian radial function is strictly positive definite, the
authors use the linear combinations of translations of the Gaussian kernel to interpolate
the scattered data on spheres in this article. Seeing that target functions are usually outside
the native spaces, and that one has to solve a large scaled system of linear equations to
obtain combinatorial coefficients of interpolant functions, the authors first probe into some
problems about interpolation with Gaussian radial functions. Then they construct quasiinterpolation
operators by Gaussian radial function, and get the degrees of approximation.
Moreover, they show the error relations between quasi-interpolation and interpolation when
they have the same basis functions. Finally, the authors discuss the construction and
approximation of the quasi-interpolant with a local support function. 相似文献
12.
In this paper, we obtain the boundedness of the fractional integral operators, the bilinear fractional integral operators and the bilinear Hilbert transform on α-modulation spaces. 相似文献
13.
Wang Shiming 《分析论及其应用》1993,9(1):82-96
In this paper it has been systematically studied the imbedding properties of fractional integral operators of periodic functions
of several variables, and isomorphic properties of fractional integral operators in the spaces of Lipschitz continuous functions.
It has also been proved that the space of fractional integration, the space of Lipschitz continuous functions and the Sobolev
space are identical in L2-norm. Results obtained here are not true for fractional integrals (or Riesz potentials) in ℝ
n
.
Supported by NNSFC 相似文献
14.
A. V. Tarasenko 《Russian Mathematics (Iz VUZ)》2013,57(1):64-71
For a mixed-type equation we study a problem with generalized fractional integrodifferentiation operators in the boundary condition. We prove its unique solvability under inequality-type conditions imposed on the known functions for various orders of fractional integrodifferentiation operators. We prove the existence of a solution to the problem by reducing the latter to a fractional differential equation. 相似文献
15.
M.C Gaer 《Journal of Mathematical Analysis and Applications》1975,50(1):135-141
For a class of complex valued functions on the real line a fractional derivative is defined which is an entire function of exponential type of the order. It is shown that these derivatives can be found by a Newton interpolation series. For a class of linear operators, a fractional derivative for their resolvents also is defined. These fractional derivatives and the fractional iterates of these operators are related and both can be found by a Newton interpolation series on the nth-order iterates of the operators. 相似文献
16.
Vakhtang Kokilashvili Mieczysław Mastyło Alexander Meskhi 《Journal of Mathematical Analysis and Applications》2015
The main aim of this paper is to study a general multisublinear operators generated by quasi-concave functions between weighted Banach function lattices. These operators, in particular, generalize the Hardy–Littlewood and fractional maximal functions playing an important role in harmonic analysis. We prove that under some general geometrical assumptions on Banach function lattices two-weight weak type and also strong type estimates for these operators are true. To derive the main results of this paper we characterize the strong type estimate for a variant of multilinear averaging operators. As special cases we provide boundedness results for fractional maximal operators in concrete function spaces. 相似文献
17.
Quasi-interpolation of radial basis functions on finite grids is a very useful strategy in approximation theory and its applications. A notable strongpoint of the strategy is to obtain directly the approximants without the need to solve any linear system of equations. For radial basis functions with Gaussian kernel, there have been more studies on the interpolation and quasi-interpolation on infinite grids. This paper investigates the approximation by quasi-interpolation operators with Gaussian kernel on the compact interval. The approximation errors for two classes of function with compact support sets are estimated. Furthermore, the approximation errors of derivatives of the approximants to the corresponding derivatives of the approximated functions are estimated. Finally, the numerical experiments are presented to confirm the accuracy of the approximations. 相似文献
18.
Milton Ferreira R. Sren Kraußhar M. Manuela Rodrigues Nelson Vieira 《Mathematical Methods in the Applied Sciences》2019,42(10):3633-3653
In this paper, we develop a fractional integro‐differential operator calculus for Clifford algebra‐valued functions. To do that, we introduce fractional analogues of the Teodorescu and Cauchy‐Bitsadze operators, and we investigate some of their mapping properties. As a main result, we prove a fractional Borel‐Pompeiu formula based on a fractional Stokes formula. This tool in hand allows us to present a Hodge‐type decomposition for the fractional Dirac operator. Our results exhibit an amazing duality relation between left and right operators and between Caputo and Riemann‐Liouville fractional derivatives. We round off this paper by presenting a direct application to the resolution of boundary value problems related to Laplace operators of fractional order. 相似文献
19.
Francis J. Narcowich Joseph D. Ward Holger Wendland. 《Mathematics of Computation》2005,74(250):743-763
In this paper we discuss Sobolev bounds on functions that vanish at scattered points in a bounded, Lipschitz domain that satisfies a uniform interior cone condition. The Sobolev spaces involved may have fractional as well as integer order. We then apply these results to obtain estimates for continuous and discrete least squares surface fits via radial basis functions (RBFs). These estimates include situations in which the target function does not belong to the native space of the RBF.
20.
某些算子和交换子在非齐型空间上的Morrey-Herz空间中的有界性 总被引:2,自引:0,他引:2
引入了非齐型空间上的齐次Morrey-Herz 空间和弱齐次Morrey-Herz空间并建立了Hardy-Littlewood极大算子,Calder\'on-Zygmund算子和分数次积分算子在齐次Morrey-Herz空间中的有界性以及在弱齐次Morrey-Herz空间中的弱型估计. 此外,还证明了$\rb$函数与Calder\'on-Zygmund算子或分数次积分算子生成的多线性交换子以及与Hardy-Littlewood极大算子相关的极大交换子在齐次Morrey-Herz空间中的有界性. 相似文献