The main purpose of this work is to establish some logarithmic estimates of optimal type in the Hardy-Sobolev space Hk,∞; k ∈ N∗ of an annular domain. These results are considered as a continuation of a previous study in the setting of the unit disk by L.Baratchart and M. Zerner, On the recovery of functions from pointwise boundary values in a Hardy-Sobolev class of the disk, J. Comput. Appl. M...

We present a unified strategy to derive Hardy–Poincaré inequalities on bounded and unbounded domains. The approach allows proving general inequality from which the classical Poincaré Hardy immediately follow. extend idea more context of variable exponent Sobolev spaces. Surprisingly, despite well-known counterexamples Fan et al. (2005) [28] , we show that modular form is actually possible provi...

The objective of this paper is to establish a new class dynamic inequalities the Hardy type which generalize and improve some recent results given in literature, we derive weighted integral on time scale.

Let BN be the unit ball in the N-dimensional complex space, for ψ, a holomorphic function in BN , and φ, a holomorphic map from BN into itself, the weighted composition operator on the weighted Hardy space H(β,BN ) is given by (Cψ,φ) f = ψ(z) f (φ(z)), where f ∈H2(β,BN ). This paper discusses the spectrum of Cψ,φ when it is compact on a certain class of weighted Hardy spaces and when the compos...

Introducing the notion of extended Schrödinger spaces, we define criticality and subcriticality forms in manner similar to recurrence transience Dirichlet forms. We show that a form is critical (resp. subcritical) if only there exists an excessive function associated semigroup defined by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext...

Marcinkiewicz multipliers are L bounded for 1 < p < ∞ on the Heisenberg group H ≃ C × R (D. Muller, F. Ricci and E. M. Stein [25], [26]). This is surprising in that this class of multipliers is invariant under a two parameter group of dilations on C × R, while there is no two parameter group of automorphic dilations on H. This lack of automorphic dilations underlies the inability of classical o...