A T(b) type theorem on the weighted Herz-type Hardy spaces and applications

2015 ◽  
Vol 289 (8-9) ◽  
pp. 1112-1130
Author(s):  
Jianmiao Ruan ◽  
Lijing Sun ◽  
Huoxiong Wu ◽  
Xiao Yu
Keyword(s):  
Hardy Spaces ◽  
Type Theorem

Hp-Maximal Regularity and Operator Valued Multipliers on Hardy Spaces

2007 ◽  
Vol 59 (6) ◽  
pp. 1207-1222 ◽  
Author(s):  
Shangquan Bu ◽  
Christian Le Merdy
Keyword(s):  
Banach Space ◽  
Cauchy Problem ◽  
Hardy Spaces ◽  
Maximal Regularity ◽  
Type Theorem ◽  
Closed Operator ◽  
Fourier Multipliers ◽  
The Cauchy Problem

AbstractWe consider maximal regularity in the Hp sense for the Cauchy problem u′(t) + Au(t) = f(t) (t ∈ ℝ), where A is a closed operator on a Banach space X and f is an X-valued function defined on ℝ. We prove that if X is an AUMD Banach space, then A satisfies Hp-maximal regularity if and only if A is Rademacher sectorial of type < . Moreover we find an operator A with Hp-maximal regularity that does not have the classical Lp-maximal regularity. We prove a related Mikhlin type theorem for operator valued Fourier multipliers on Hardy spaces Hp(ℝ X), in the case when X is an AUMD Banach space.

scholarly journals Universality on higher order Hardy spaces

2005 ◽  
Vol 71 (1) ◽  
pp. 17-28
Author(s):  
L. Bernal-González ◽  
A. Bonilla ◽  
M. C. Calderón-Moreno
Keyword(s):  
Unit Disk ◽  
Hardy Spaces ◽  
Composition Operators ◽  
Type Theorem ◽  
Higher Order ◽  
Interpolating Sequences ◽  
Bounded Functions

We prove a Seidel-Walsh-type theorem about the universality of a sequence of derivation-composition operators generated by automorphisms of the unit disk in the setting of the higher order Hardy spaces. Moreover, some related positive or negative assertions involving interpolating sequences and sequences between two tangent circles are established for the class of bounded functions in the unit disk. Our statements improve earlier ones due to Herzog and to the first and third authors.

Nehari-Type Theorem for Non-commutative Hardy Spaces

2016 ◽  
Vol 27 (3) ◽  
pp. 1789-1802 ◽  
Author(s):  
F. Sukochev ◽  
K. Tulenov ◽  
D. Zanin
Keyword(s):  
Hardy Spaces ◽  
Type Theorem

scholarly journals Hadamard Multipliers and Abel Dual of Hardy Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Paweł Mleczko
Keyword(s):  
Hardy Spaces ◽  
Convolution Operator ◽  
Type Theorem ◽  
Rearrangement Invariant Spaces ◽  
Hardy Classes ◽  
Measurable Functions ◽  
Invariant Spaces

The paper is devoted to the study of Hadamard multipliers of functions from the abstract Hardy classes generated by rearrangement invariant spaces. In particular the relation between the existence of such multiplier and the boundedness of the appropriate convolution operator on spaces of measurable functions is presented. As an application, the description of Hadamard multipliers intoH∞is given and the Abel type theorem for mentioned Hardy spaces is proved.

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