scholarly journals Embedding Hardy spaces $H^p$ into tent spaces and generalized integration operators

2022 ◽  
Author(s):  
Ruishen Qian ◽  
Xiangling Zhu
Keyword(s):  
Hardy Spaces ◽  
Tent Spaces

scholarly journals Potential maps, Hardy spaces, and tent spaces on special Lipschitz domains

2013 ◽  
Vol 57 ◽  
pp. 295-331
Author(s):  
M. Costabel ◽  
A. McIntosh ◽  
R. J. Taggart
Keyword(s):  
Hardy Spaces ◽  
Lipschitz Domains ◽  
Tent Spaces

scholarly journals Carleson embeddings

1996 ◽  
Vol 1 (2) ◽  
pp. 193-201
Author(s):  
Helmut J. Heiming
Keyword(s):  
Hardy Spaces ◽  
Unit Disc ◽  
Carleson Measure ◽  
Composition Operators ◽  
Function Spaces ◽  
Main Topic ◽  
Embedding Theorems ◽  
Absolutely Continuous ◽  
Tent Spaces ◽  
Similar Kind

In this paper we discuss several operator ideal properties for so called Carleson embeddings of tent spaces into specificL q(μ)-spaces, whereμis a Carleson measure on the complex unit disc. Characterizing absolutelyq-summing, absolutely continuous andq-integral Carleson embeddings in terms of the underlying measure is our main topic. The presented results extend and integrate results especially known for composition operators on Hardy spaces as well as embedding theorems for function spaces of similar kind.

scholarly journals ON VECTOR-VALUED TENT SPACES AND HARDY SPACES ASSOCIATED WITH NON-NEGATIVE SELF-ADJOINT OPERATORS

2015 ◽  
Vol 58 (3) ◽  
pp. 689-716 ◽  
Author(s):  
MIKKO KEMPPAINEN
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Integral Operators ◽  
Complex Interpolation ◽  
Tent Spaces ◽  
Tent Space ◽  
Holomorphic Functional Calculus ◽  
Adjoint Operators ◽  
Vector Valued

AbstractIn this paper, we study Hardy spaces associated with non-negative self-adjoint operators and develop their vector-valued theory. The complex interpolation scales of vector-valued tent spaces and Hardy spaces are extended to the endpoint p=1. The holomorphic functional calculus of L is also shown to be bounded on the associated Hardy space H1L(X). These results, along with the atomic decomposition for the aforementioned space, rely on boundedness of certain integral operators on the tent space T1(X).

HARDY SPACES, APPROXIMATION ISSUES AND BOUNDARY VALUE PROBLEMS

2018 ◽  
Vol 9 (3) ◽  
pp. 85-94
Author(s):  
V.I. Vlasov ◽  
◽  
◽  
Keyword(s):  
Boundary Value Problems ◽  
Hardy Spaces ◽  
Boundary Value

Fourier transform of anisotropic mixed-norm Hardy spaces

2021 ◽  
Vol 16 (1) ◽  
pp. 119-139
Author(s):  
Long Huang ◽  
Der-Chen Chang ◽  
Dachun Yang
Keyword(s):  
Fourier Transform ◽  
Hardy Spaces ◽  
Mixed Norm

Multi-parameter hardy spaces via discrete Littlewood-Paley theory

2010 ◽  
Vol 26 (2) ◽  
pp. 122-139 ◽  
Author(s):  
Zhuoping Ruan
Keyword(s):  
Hardy Spaces

scholarly journals Variable Anisotropic Hardy Spaces with Variable Exponents

2021 ◽  
Vol 9 (1) ◽  
pp. 65-89
Author(s):  
Zhenzhen Yang ◽  
Yajuan Yang ◽  
Jiawei Sun ◽  
Baode Li
Keyword(s):  
Hardy Spaces ◽  
Variable Exponent ◽  
Atomic Decomposition ◽  
Integral Operators ◽  
Moment Condition ◽  
Variable Exponents ◽  
Hölder Continuous ◽  
Multi Level ◽  
The Moment ◽  
Variable Anisotropy

Abstract Let p(·) : ℝ n → (0, ∞] be a variable exponent function satisfying the globally log-Hölder continuous and let Θ be a continuous multi-level ellipsoid cover of ℝ n introduced by Dekel et al. [12]. In this article, we introduce highly geometric Hardy spaces Hp (·)(Θ) via the radial grand maximal function and then obtain its atomic decomposition, which generalizes that of Hardy spaces Hp (Θ) on ℝ n with pointwise variable anisotropy of Dekel et al. [16] and variable anisotropic Hardy spaces of Liu et al. [24]. As an application, we establish the boundedness of variable anisotropic singular integral operators from Hp (·)(Θ) to Lp (·)(ℝ n ) in general and from Hp (·)(Θ) to itself under the moment condition, which generalizes the previous work of Bownik et al. [6] on Hp (Θ).

Boundedness of multi-parameter pseudo-differential operators on multi-parameter local Hardy spaces

2020 ◽  
Vol 32 (4) ◽  
pp. 919-936 ◽  
Author(s):  
Jiao Chen ◽  
Wei Ding ◽  
Guozhen Lu
Keyword(s):  
Hardy Spaces ◽  
Differential Operators ◽  
Integral Operators ◽  
Fourier Multipliers ◽  
Regularity Of Solutions ◽  
Local Version ◽  
Fourier Integral Operators ◽  
Pseudo Differential Operators ◽  
Local Hardy Spaces ◽  
The One

AbstractAfter the celebrated work of L. Hörmander on the one-parameter pseudo-differential operators, the applications of pseudo-differential operators have played an important role in partial differential equations, geometric analysis, harmonic analysis, theory of several complex variables and other branches of modern analysis. For instance, they are used to construct parametrices and establish the regularity of solutions to PDEs such as the {\overline{\partial}} problem. The study of Fourier multipliers, pseudo-differential operators and Fourier integral operators has stimulated further such applications. It is well known that the one-parameter pseudo-differential operators are {L^{p}({\mathbb{R}^{n}})} bounded for {1<p<\infty}, but only bounded on local Hardy spaces {h^{p}({\mathbb{R}^{n}})} introduced by Goldberg in [D. Goldberg, A local version of real Hardy spaces, Duke Math. J. 46 1979, 1, 27–42] for {0<p\leq 1}. Though much work has been done on the {L^{p}(\mathbb{R}^{n_{1}}\times\mathbb{R}^{n_{2}})} boundedness for {1<p<\infty} and Hardy {H^{p}(\mathbb{R}^{n_{1}}\times\mathbb{R}^{n_{2}})} boundedness for {0<p\leq 1} for multi-parameter Fourier multipliers and singular integral operators, not much has been done yet for the boundedness of multi-parameter pseudo-differential operators in the range of {0<p\leq 1}. The main purpose of this paper is to establish the boundedness of multi-parameter pseudo-differential operators on multi-parameter local Hardy spaces {h^{p}(\mathbb{R}^{n_{1}}\times\mathbb{R}^{n_{2}})} for {0<p\leq 1} recently introduced by Ding, Lu and Zhu in [W. Ding, G. Lu and Y. Zhu, Multi-parameter local Hardy spaces, Nonlinear Anal. 184 2019, 352–380].

Sign in / Sign up

Export Citation Format

Share Document