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.

Singular Integral Operators and Essential Commutativity on the Sphere

2010 ◽  
Vol 62 (4) ◽  
pp. 889-913 ◽  
Author(s):  
Jingbo Xia
Keyword(s):  
Hardy Space ◽  
Singular Integral ◽  
Unit Sphere ◽  
Toeplitz Operators ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Essential Commutant

AbstractLet 𝒯 be the C*-algebra generated by the Toeplitz operators {T𝜑 : 𝜑 Є L∞(S, dσ)} on the Hardy space H2(S) of the unit sphere in Cn. It is well known that 𝒯 is contained in the essential commutant of {T𝜑 : 𝜑 Є VMO∩L∞(S, dσ)}. We show that the essential commutant of {T𝜑 : 𝜑 Є VMO∩L∞(S, dσ)} is strictly larger than 𝒯.

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 On an extension of singular integrals along manifolds of finite type

2006 ◽  
Vol 2006 ◽  
pp. 1-16
Author(s):  
Abdelnaser Al-Hasan ◽  
Dashan Fan
Keyword(s):  
Sobolev Space ◽  
Finite Type ◽  
Singular Integral ◽  
Lebesgue Space ◽  
Compact Manifold ◽  
Singular Integrals ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Homogeneous Sobolev Space

We extend theLp-boundedness of a class of singular integral operators under theH1kernel condition on a compact manifold from the homogeneous Sobolev spaceL˙αp(ℝn)to the Lebesgue spaceLp(ℝn).

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.

$C^\ast$-Algebras of singular integral operators and Toeplitz operators associated with measure-preserving transformations

1998 ◽  
Vol 18 (2) ◽  
pp. 487-502
Author(s):  
JINGBO XIA
Keyword(s):  
Dynamical Systems ◽  
Singular Integral ◽  
Toeplitz Operators ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Measure Preserving Transformations

We show in the setting of measure-theoretical dynamical systems that certain singular integral operators and Toeplitz operators with the same coefficients but represented on different $L^2$-spaces are $C^\ast $-algebraically equivalent.

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