共查询到20条相似文献,搜索用时 31 毫秒
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In this paper, applying the atomic decomposition and molecular characterization of the real weighted Hardy spaces , we give the weighted boundedness of the homogeneous fractional integral operator from to , and from to . 相似文献
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On commutators of Marcinkiewicz integrals with rough kernel 总被引:2,自引:0,他引:2
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H. Movahedi-Lankarani R. Wells 《Journal of Mathematical Analysis and Applications》2003,285(1):299-320
The C1-Weierstrass approximation theorem is proved for any compact subset X of a Hilbert space . The same theorem is also proved for Whitney 1-jets on X when X satisfies the following further condition: There exist finite dimensional linear subspaces such that ?n?1Hn is dense in and πn(X)=X∩Hn for each n?1. Here, is the orthogonal projection. It is also shown that when X is compact convex with and satisfies the above condition, then C1(X) is complete if and only if the C1-Whitney extension theorem holds for X. Finally, for compact subsets of , an extension of the C1-Weierstrass approximation theorem is proved for C1 maps with compact derivatives. 相似文献
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Let and be standard operator algebras on infinite dimensional complex Banach spaces X and Y, respectively, and let Φ be a unital additive surjection from onto . We introduce thirteen parts of the spectrum for elements in and , and prove that if Φ preserves any one of these parts of the spectrum, then it is either an isomorphism or an anti-isomorphism. 相似文献
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The Bohl-Bohr-Amerio-Kadets theorem states that the indefinite integral y=Pφ of an almost periodic (ap) is again ap if y is bounded and the Banach space X does not contain a subspace isomorphic to c0. This is here generalized in several directions: Instead of it holds also for φ defined only on a half-line , instead of ap functions abstract classes with suitable properties are admissible, can be weakened to φ in some “mean” class , then ; here contains all f∈L1loc with in for all h>0 (usually strictly); furthermore, instead of boundedness of y mean boundedness, y in some , or in , ergodic functions, suffices. The Loomis-Doss result on the almost periodicity of a bounded Ψ for which all differences Ψ(t+h)−Ψ(t) are ap for h>0 is extended analogously, also to higher order differences. Studying “difference spaces” in this connection, we obtain decompositions of the form: Any bounded measurable function is the sum of a bounded ergodic function and the indefinite integral of a bounded ergodic function. The Bohr-Neugebauer result on the almost periodicity of bounded solutions y of linear differential equations P(D)y=φ of degree m with ap φ is extended similarly for ; then provided, for example, y is in some with U=L∞ or is totally ergodic and, for the half-line, Reλ?0 for all eigenvalues P(λ)=0. Analogous results hold for systems of linear differential equations. Special case: φ bounded and Pφ ergodic implies Pφ bounded. If all Reλ>0, there exists a unique solution y growing not too fast; this y is in if , for quite general . 相似文献
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Jian-Ping Fang 《Journal of Mathematical Analysis and Applications》2007,332(2):1393-1407
In this paper, we construct a new q-exponential operator and obtain some operator identities. Using these operator identities, we give a formal extension of Jackson's transformation formula. A formal extension of Bailey's summation and an extension of the Sears terminating balanced transformation formula are also derived by our operator method. In addition, we also derive several interesting a formal extensions involving multiple sum about three terms of Sears transformation formula and Heine's transformation formula. 相似文献
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Nguyen Huy Chieu 《Journal of Mathematical Analysis and Applications》2008,341(1):247-258
We compute the limiting subdifferential of the indefinite integral of the form where f is an essentially bounded measurable function, or a function continuous on an interval containing (except for, possibly, ), or a step-function which has a countable number of steps around . The related problem of computing the Aumann integral of the limiting subdifferential mapping ∂f(⋅), where f is a Lipschitz real function defined on an open set U⊂Rn, is also investigated. 相似文献
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Qi-Xiang Yang 《Journal of Mathematical Analysis and Applications》2011,377(1):253-258
We study in this paper some relations between Hardy spaces which are defined by non-smooth approximate identity ?(x), and the end-point Triebel-Lizorkin spaces (1?q?∞). First, we prove that for compact ? which satisfies a slightly weaker condition than Fefferman and Stein's condition. Then we prove that non-trivial Hardy space defined by approximate identity ? must contain Besov space . Thirdly, we construct certain functions and a function such that Daubechies wavelet function but . 相似文献
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Taekyun Kim 《Journal of Mathematical Analysis and Applications》2007,329(2):1472-1481
In this paper, we give an explicit p-adic expansion of
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U. Raitums 《Journal of Mathematical Analysis and Applications》2011,376(2):675-685
The paper considers a slightly modified notion of the Γ-convergence of convex functionals in uniformly convex Banach spaces and establishes that under standard coercitivity and growth conditions the Γ-convergence of a sequence of functionals {Fj} to implies that the corresponding sequence of dual functionals converges in an analogous sense to the dual to functional . 相似文献
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Dong Joo Moon Seoung Dal Jung 《Journal of Mathematical Analysis and Applications》2008,342(1):354-360
Let M be a complete Riemannian manifold and let N be a Riemannian manifold of non-positive sectional curvature. Assume that at all x∈M and at some point x0∈M, where μ0>0 is the least eigenvalue of the Laplacian acting on L2-functions on M. Let 2?q?p. Then any q-harmonic map of finite q-energy is constant. Moreover, if N is a Riemannian manifold of non-positive scalar curvature, then any q-harmonic morphism of finite q-energy is constant. 相似文献