共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
We apply the techniques of monotone and relative rearrangements to the nonrearrangement invariant spaces Lp()(Ω) with variable exponent. In particular, we show that the maps uLp()(Ω)→k(t)u*Lp*()(0,measΩ) and uLp()(Ω)→u*Lp*()(0,measΩ) are locally -Hölderian (u* (resp. p*) is the decreasing (resp. increasing) rearrangement of u (resp. p)). The pointwise relations for the relative rearrangement are applied to derive the Sobolev embedding with eventually discontinuous exponents. 相似文献
3.
In this article we introduce Besov spaces with variable smoothness and integrability indices. We prove independence of the choice of basis functions, as well as several other basic properties. We also give Sobolev-type embeddings, and show that our scale contains variable order Hölder-Zygmund spaces as special cases. We provide an alternative characterization of the Besov space using approximations by analytic functions. 相似文献
4.
In this article we study variable exponent Sobolev spaces on Riemannian manifolds. The spaces are examined in the case of compact manifolds. Continuous and compact embeddings are discussed. The paper contains an example of the application of the theory to elliptic equations on compact manifolds. 相似文献
5.
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
6.
In this article we introduce Triebel-Lizorkin spaces with variable smoothness and integrability. Our new scale covers spaces with variable exponent as well as spaces of variable smoothness that have been studied in recent years. Vector-valued maximal inequalities do not work in the generality which we pursue, and an alternate approach is thus developed. Using it we derive molecular and atomic decomposition results and show that our space is well-defined, i.e., independent of the choice of basis functions. As in the classical case, a unified scale of spaces permits clearer results in cases where smoothness and integrability interact, such as Sobolev embedding and trace theorems. As an application of our decomposition we prove optimal trace theorem in the variable indices case. 相似文献
7.
N.G. Samko S.G. Samko B.G. Vakulov 《Journal of Mathematical Analysis and Applications》2007,335(1):560-583
For the Riesz potential operator Iα there are proved weighted estimates
8.
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
9.
10.
In this article, by extending classical Dellacherie's theorem on stochastic sequences to variable exponent spaces, we prove that the famous Burkholder-Gundy-Davis inequality holds for martingales in variable exponent Hardy spaces. We also obtain the variable exponent analogues of several martingale inequalities in classical theory, including convexity lemma, Chevalier's inequality and the equivalence of two kinds of martingale spaces with predictable control. Moreover, under the regular condition on σ-algebra sequence we prove the equivalence between five kinds of variable exponent martingale Hardy spaces. 相似文献
11.
In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Littlewood-Paley operators, including the parameterized Lusin area integrals and the parameterized Littlewood-Paley g*λ-functions, is established on the Lebesgue spaces with variable exponent. Furthermore,the boundedness of their commutators generated respectively by BMO functions and Lipschitz functions are also obtained. 相似文献
12.
Ferenc Weisz 《Mathematische Nachrichten》2023,296(4):1687-1705
Let be a measurable function defined on and . In this paper, we generalize the Hardy–Littlewood maximal operator. In the definition, instead of cubes or balls, we take the supremum over all rectangles the side lengths of which are in a cone-like set defined by a given function ψ. Moreover, instead of the integral means, we consider the -means. Let and satisfy the log-Hülder condition and . Then, we prove that the maximal operator is bounded on if and is bounded from to the weak if . We generalize also the theorem about the Lebesgue points. 相似文献
13.
Sadulla Z. Jafarov 《复变函数与椭圆型方程》2018,63(10):1444-1458
In the present work, we investigate the approximation problems of the functions by Fejér, and Zygmund means of Fourier trigonometric series in weighted Lebesgue spaces with variable exponents and of the functions by Fejér and Abel–Poisson sums of Faber series in weighted Smirnov classes with variable exponents defined on simply connected domains with a Dini-smooth boundary of the complex plane. 相似文献
14.
15.
Ferenc Weisz 《Journal of Mathematical Analysis and Applications》2008,344(1):42-54
A general summability method, the so-called θ-summability is considered for multi-dimensional Fourier transforms and Fourier series. A new inequality for the Hardy-Littlewood maximal function is verified. It is proved that if the Fourier transform of θ is in a Herz space, then the restricted maximal operator of the θ-means of a distribution is of weak type (1,1), provided that the supremum in the maximal operator is taken over a cone-like set. From this it follows that over a cone-like set a.e. for all f∈L1(Rd). Moreover, converges to f(x) over a cone-like set at each Lebesgue point of f∈L1(Rd) if and only if the Fourier transform of θ is in a suitable Herz space. These theorems are extended to Wiener amalgam spaces as well. The Riesz and Weierstrass summations are investigated as special cases of the θ-summation. 相似文献
16.
17.
Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered. 相似文献
18.
Jing-shi Xu 《Czechoslovak Mathematical Journal》2007,57(1):13-27
The boundednees of multilinear commutators of Calderón-Zygmund singular integrals on Lebesgue spaces with variable exponent
is obtained. The multilinear commutators of generalized Hardy-Littlewood maximal operator are also considered. 相似文献
19.
20.
For the Riesz potential of variable order over bounded domains in Euclidean space, we prove the boundedness result from variable exponent Morrey spaces to variable exponent Campanato spaces. A special attention is paid to weaken assumptions on variability of the Riesz potential. 相似文献