Equivalence of Sobolev Norms Involving Generalized Hardy Operators

On certain fractional calculus operators involving generalized Mittag-Leffler function

The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators a...

Generalized composition operators on weighted Hardy spaces

Norms of Composition Operators on the Hardy Space

Research supported in part by National Science Foundation grant DMS-9401206. Appel and Thrall were supported by the Foundation's REU program for work they performed as undergraduate assistants to Bourdon. We show that the norm of a composition operator on the classical Hardy space H2 cannot be computed using only the set of H2 reproducing kernels, answering a question raised by Cowen and MacCluer.

Norms of Composition Operators on Weighted Hardy Spaces

The norm of a bounded composition operator induced by a disc automorphism is estimated on weighted Hardy spaces H(β) in which the classical Hardy space is continuously embedded. The estimate obtained is accurate in the sense that it provides the exact norm for particular instances of the sequence β. As a by-product of our results, an estimate for the norm of any bounded composition operator on ...

On Hardy-sobolev Embedding

1. Interpolation inequalities. A classical problem in analysis is to understand how “smoothness” controls norms that measure the “size” of functions. Maz’ya recognized in his classic text on Sobolev spaces the intrinsic importance of inequalities that would refine both Hardy’s inequality and Sobolev embedding. Dilation invariance and group symmetry play an essential role in determining sharp co...