Singular Integral Operators and Maximal Functions with Hardy Space Kernels

2021 ◽  
Keyword(s):  
Hardy Space ◽  
Singular Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Maximal Functions

On a Class of Singular Integral Operators With Rough Kernels

2006 ◽  
Vol 49 (1) ◽  
pp. 3-10 ◽  
Author(s):  
Ahmad Al-Salman
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Maximal Functions ◽  
Rough Kernels ◽  
Block Spaces ◽  
Size Condition

AbstractIn this paper, we study the Lp mapping properties of a class of singular integral operators with rough kernels belonging to certain block spaces. We prove that our operators are bounded on Lp provided that their kernels satisfy a size condition much weaker than that for the classical Calderón–Zygmund singular integral operators. Moreover, we present an example showing that our size condition is optimal. As a consequence of our results, we substantially improve a previously known result on certain maximal functions.

scholarly journals Lp estimates for maximal functions along surfaces of revolution on product spaces

2019 ◽  
Vol 17 (1) ◽  
pp. 1361-1373 ◽  
Author(s):  
Mohammed Ali ◽  
Musa Reyyashi
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Maximal Functions ◽  
Maximal Operators ◽  
Product Spaces ◽  
Surfaces Of Revolution ◽  
Lp Estimates ◽  
Block Space

Abstract This paper is concerned with establishing Lp estimates for a class of maximal operators associated to surfaces of revolution with kernels in Lq(Sn−1 × Sm−1), q > 1. These estimates are used in extrapolation to obtain the Lp boundedness of the maximal operators and the related singular integral operators when their kernels are in the L(logL)κ(Sn−1 × Sm−1) or in the block space $\begin{array}{} B^{0,\kappa-1}_ q \end{array}$(Sn−1 × Sm−1). Our results substantially improve and extend some known results.

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 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 Brown-Halmos Type Theorems of Weighted Toeplitz Operators

1998 ◽  
Vol 41 (2) ◽  
pp. 196-206 ◽  
Author(s):  
Takahiko Nakazi
Keyword(s):  
Hardy Space ◽  
Singular Integral ◽  
Lebesgue Space ◽  
Toeplitz Operators ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Weighted Hardy Space

AbstractThe spectra of the Toeplitz operators on the weighted Hardy space H2(Wdθ / 2π) and the Hardy space Hp(dθ / 2π), and the singular integral operators on the Lebesgue space L2(dθ / 2π) are studied. For example, the theorems of Brown-Halmos type and Hartman-Wintner type are studied.

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