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.

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.

On orthogonality in nonseparable rearrangement invariant spaces

2021 ◽  
Vol 212 (11) ◽  
Author(s):  
Sergei Vladimirovich Astashkin ◽  
Evgenii Mikhailovich Semenov
Keyword(s):  
Rearrangement Invariant Spaces ◽  
Invariant Spaces

Orthogonal Elements in Nonseparable Rearrangement Invariant Spaces

2020 ◽  
Vol 102 (3) ◽  
pp. 449-450
Author(s):  
S. V. Astashkin ◽  
E. M. Semenov
Keyword(s):  
Rearrangement Invariant Spaces ◽  
Invariant Spaces

Hermite Conjugate Functions and Rearrangement Invariant Spaces

1973 ◽  
Vol 16 (3) ◽  
pp. 377-380 ◽  
Author(s):  
Kenneth F. Andersen
Keyword(s):  
Weak Type ◽  
Conjugate Function ◽  
Poisson Integral ◽  
Conjugate Functions ◽  
Rearrangement Invariant Spaces ◽  
Image Position ◽  
Invariant Spaces

The Hermite conjugate Poisson integral of a given f ∊ L1(μ), dμ(y)= exp(—y2) dy, was defined by Muckenhoupt [5, p. 247] aswhereIf the Hermite conjugate function operator T is defined by (Tf) a.e., then one of the main results of [5] is that T is of weak-type (1, 1) and strongtype (p,p) for all p>l.

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