scholarly journals Herz-Morrey-Hardy Spaces with Variable Exponents and Their Applications

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
Jingshi Xu ◽  
Xiaodi Yang
Keyword(s):  
Singular Integral ◽  
Hardy Spaces ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Variable Exponents

The authors introduce Herz-Morrey-Hardy spaces with variable exponents and establish the characterization of these spaces in terms of atom. Applying the characterization, the authors obtain the boundedness of some singular integral operators on these spaces.

scholarly journals Two examples related to conical energies

2022 ◽  
Vol 47 (1) ◽  
pp. 261-281
Author(s):  
Damian Dąbrowski
Keyword(s):  
Singular Integral ◽  
Recent Article ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
The Other ◽  
Independent Interest ◽  
Sufficient Condition ◽  
Lipschitz Graphs ◽  
Big Pieces

In a recent article (2021) we introduced and studied conical energies. We used them to prove three results: a characterization of rectifiable measures, a characterization of sets with big pieces of Lipschitz graphs, and a sufficient condition for boundedness of nice singular integral operators. In this note we give two examples related to sharpness of these results. One of them is due to Joyce and Mörters (2000), the other is new and could be of independent interest as an example of a relatively ugly set containing big pieces of Lipschitz graphs.

scholarly journals Boundedness of Singular Integrals on Hardy Type Spaces Associated with Schrödinger Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Jianfeng Dong ◽  
Jizheng Huang ◽  
Heping Liu
Keyword(s):  
Molecular Characterization ◽  
Singular Integral ◽  
Maximal Function ◽  
Singular Integrals ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Hardy Type ◽  
Type Spaces ◽  
Reverse Hölder

LetL=-Δ+Vbe a Schrödinger operator onRn,n≥3, whereV≢0is a nonnegative potential belonging to the reverse Hölder classBn/2. The Hardy type spacesHLp, n/(n+δ) <p≤1,for someδ>0, are defined in terms of the maximal function with respect to the semigroup{e-tL}t>0. In this paper, we investigate the bounded properties of some singular integral operators related toL, such asLiγand∇L-1/2, on spacesHLp. We give the molecular characterization ofHLp, which is used to establish theHLp-boundedness of singular integrals.

Oscillatory singular integral operators with Hölder class kernels on Hardy spaces

2019 ◽  
Vol 31 (2) ◽  
pp. 535-542
Author(s):  
Yibiao Pan
Keyword(s):  
Singular Integral ◽  
Hardy Spaces ◽  
Singular Integrals ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Oscillatory Singular Integral ◽  
Hölder Class ◽  
Holder Class ◽  
Oscillatory Singular Integrals

AbstractA sharp logarithmic bound is established for the {H^{1}}-norm of oscillatory singular integrals with quadratic phases and Hölder class kernels. Prior results had relied on a {C^{1}}-assumption on the kernel.

scholarly journals Boundedness for a Class of Singular Integral Operators on Both Classical and Product Hardy Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Chaoqiang Tan
Keyword(s):  
Singular Integral ◽  
Hardy Spaces ◽  
General Class ◽  
Integral Operators ◽  
Singular Integral Operators

We found that the classical Calderón-Zygmund singular integral operators are bounded on both the classical Hardy spaces and the product Hardy spaces. The purpose of this paper is to extend this result to a more general class. More precisely, we introduce a class of singular integral operators including the classical Calderón-Zygmund singular integral operators and show that they are bounded on both the classical Hardy spaces and the product Hardy spaces.

scholarly journals The Boundedness on Mixed Hardy Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Wei Ding ◽  
Meidi Qin ◽  
Yueping Zhu
Keyword(s):  
Singular Integral ◽  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Direct Method ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
A Direct Method

The boundedness of operators on Hardy spaces is usually given by atomic decomposition. In this paper, we obtain the boundedness of singular integral operators in mixed Journé class on mixed Hardy spaces by a direct method.

scholarly journals Some weighted estimates for imaginary powers of Laplace operators

2002 ◽  
Vol 65 (1) ◽  
pp. 129-135 ◽  
Author(s):  
Hendra Gunawan
Keyword(s):  
Laplace Operator ◽  
Singular Integral ◽  
Hardy Spaces ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Lebesgue Spaces ◽  
Weighted Hardy Spaces ◽  
Weighted Estimates ◽  
Imaginary Powers ◽  
The Laplace Operator

We study the boundedness of singular integral operators that are imaginary powers of the Laplace operator in Rn, especially from weighted Hardy spaces to weighted Lebesgue spaces where 0 < p ≤ 1. In particular, we prove some estimates for these operators when 0 < p ≤ 1 and w is in the Muckenhoupt's class Aq, for some q > 1.

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