scholarly journals Herz-Type Hardy Spaces Associated with Operators

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Yan Chai ◽  
Yaoyao Han ◽  
Kai Zhao
Keyword(s):  
Differential Operator ◽  
Hardy Space ◽  
Singular Integral ◽  
Hardy Spaces ◽  
Integral Operators ◽  
Singular Integral Operators

Suppose L is a nonnegative, self-adjoint differential operator. In this paper, we introduce the Herz-type Hardy spaces associated with operator L. Then, similar to the atomic and molecular decompositions of classical Herz-type Hardy spaces and the Hardy space associated with operators, we prove the atomic and molecular decompositions of the Herz-type Hardy spaces associated with operator L. As applications, the boundedness of some singular integral operators on Herz-type Hardy spaces associated with operators is obtained.

scholarly journals B-maximal commutators, commutators of B-singular integral operators and B-Riesz potentials on B-Morrey spaces

2020 ◽  
Vol 18 (1) ◽  
pp. 715-730
Author(s):  
Javanshir J. Hasanov ◽  
Rabil Ayazoglu ◽  
Simten Bayrakci
Keyword(s):  
Differential Operator ◽  
Singular Integral ◽  
Riesz Potential ◽  
Type Theorem ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Singular Integral Operators ◽  
Sobolev Type ◽  
Riesz Potentials ◽  
Bessel Differential Operator

Abstract In this article, we consider the Laplace-Bessel differential operator {\Delta }_{{B}_{k,n}}=\mathop{\sum }\limits_{i=1}^{k}\left(\frac{{\partial }^{2}}{\partial {x}_{i}^{2}}+\frac{{\gamma }_{i}}{{x}_{i}}\frac{\partial }{\partial {x}_{i}}\right)+\mathop{\sum }\limits_{i=k+1}^{n}\frac{{\partial }^{2}}{\partial {x}_{i}^{2}},{\gamma }_{1}\gt 0,\ldots ,{\gamma }_{k}\gt 0. Furthermore, we define B-maximal commutators, commutators of B-singular integral operators and B-Riesz potentials associated with the Laplace-Bessel differential operator. Moreover, we also obtain the boundedness of the B-maximal commutator {M}_{b,\gamma } and the commutator {[}b,{A}_{\gamma }] of the B-singular integral operator and Hardy-Littlewood-Sobolev-type theorem for the commutator {[}b,{I}_{\alpha ,\gamma }] of the B-Riesz potential on B-Morrey spaces {L}_{p,\lambda ,\gamma } , when b\in {\text{BMO}}_{\gamma } .

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.

The Hardy Space H1 on Manifolds and Submanifolds

1972 ◽  
Vol 24 (5) ◽  
pp. 915-925 ◽  
Author(s):  
Robert S. Strichartz
Keyword(s):  
Partial Differential Equations ◽  
Hardy Space ◽  
Euclidean Space ◽  
Differential Equations ◽  
Singular Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Riesz Transforms ◽  
Partial Differential ◽  
Integrable Functions

It is well-known that the space L1(Rn) of integrable functions on Euclidean space fails to be preserved by singular integral operators. As a result the rather large Lp theory of partial differential equations also fails for p = 1. Since L1 is such a natural space, many substitute spaces have been considered. One of the most interesting of these is the space we will denote by H1(Rn) of integrable functions whose Riesz transforms are integrable.

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.

Bn-maximal operator and Bn-singular integral operators on variable exponent Lebesgue spaces

2020 ◽  
Vol 70 (4) ◽  
pp. 893-902
Author(s):  
Ismail Ekincioglu ◽  
Vagif S. Guliyev ◽  
Esra Kaya
Keyword(s):  
Differential Operator ◽  
Singular Integral ◽  
Maximal Operator ◽  
Variable Exponent ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Lebesgue Spaces ◽  
Variable Exponent Lebesgue Spaces ◽  
Bessel Differential Operator

AbstractIn this paper, we prove the boundedness of the Bn maximal operator and Bn singular integral operators associated with the Laplace-Bessel differential operator ΔBn on variable exponent Lebesgue spaces.

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.

scholarly journals Boundedness of Singular Integral Operators with Variable Kernels on Weighted Weak Hardy Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Hua Wang
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Variable Kernel ◽  
Decomposition Theory

Let TΩ be the singular integral operator with variable kernel Ω(x,z). In this paper, by using the atomic decomposition theory of weighted weak Hardy spaces, we will obtain the boundedness properties of TΩ on these spaces, under some Dini type conditions imposed on the variable kernel Ω(x,z).

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