Weighted Morrey-Herz spaces and applications.
We discuss the characterization of the inequality (RN+ fq u)1/q C (RN+ fp v )1/p, 0<q, p <, for monotone functions and nonnegative weights and and . We prove a new multidimensional integral modular inequality for monotone functions. This inequality generalizes and unifies some recent results in one and several dimensions.
Let X be a homogeneous space and let E be a UMD Banach space with a normalized unconditional basis . Given an operator T from to L¹(X), we consider the vector-valued extension T̃ of T given by . We prove a weighted integral inequality for the vector-valued extension of the Hardy-Littlewood maximal operator and a weighted Fefferman-Stein inequality between the vector-valued extensions of the Hardy-Littlewood and the sharp maximal operators, in the context of Orlicz spaces. We give sufficient...
We give a characterization of the weights (u,w) for which the Hardy-Littlewood maximal operator is bounded from the Orlicz space L_Φ(u) to L_Φ(w). We give a characterization of the weight functions w (respectively u) for which there exists a nontrivial u (respectively w > 0 almost everywhere) such that the Hardy-Littlewood maximal operator is bounded from the Orlicz space L_Φ(u) to L_Φ(w).
Necessary and sufficient conditions are given for the Hardy-Littlewood maximal operator to be bounded on a weighted Orlicz space when the complementary Young function satisfies . Such a growth condition is shown to be necessary for any weighted integral inequality to occur. Weak-type conditions are also investigated.
The analytic-spectral structure of the commutant of a weighted shift operator defined on a lp space (1 ≤ p < ∞) is studied. The cases unilateral, bilateral and quasinilpotent are treated. We apply the results to study certain questions related to unicellularity, strictly cyclicity and the existence of hyperinvariant subspaces.
We deal with weighted spaces and HV(U) of holomorphic functions defined on a balanced open subset U of a Banach space X. We give conditions on the weights to ensure that the weighted spaces of m-homogeneous polynomials constitute a Schauder decomposition for them. As an application, we study their reflexivity. We also study the existence of a predual. Several examples are provided.
We study sub-Bergman Hilbert spaces in the weighted Bergman space . We generalize the results already obtained by Kehe Zhu for the standard Bergman space .