Hardy Space Estimate for the Product of Singular Integrals

2000 ◽  
Vol 52 (2) ◽  
pp. 381-411 ◽  
Author(s):  
Akihiko Miyachi
Keyword(s):  
Hardy Space ◽  
Sobolev Space ◽  
Singular Integrals ◽  
Fractional Integrals ◽  
Multilinear Operators ◽  
Finite Sums

AbstractHp estimate for the multilinear operators which are finite sums of pointwise products of singular integrals and fractional integrals is given. An application to Sobolev space and some examples are also given.

scholarly journals Hardy Space Estimates for Multilinear Operators, I

1992 ◽  
pp. 45-67 ◽  
Author(s):  
Ronald Coifman ◽  
Loukas Grafakos
Keyword(s):  
Hardy Space ◽  
Multilinear Operators

BOUNDEDNESS OF SEVERAL INTEGRAL OPERATORS WITH BOUNDED VARIABLE KERNELS ON HARDY AND WEAK HARDY SPACES

2013 ◽  
Vol 24 (12) ◽  
pp. 1350095 ◽  
Author(s):  
HUA WANG
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Variable Kernel ◽  
Marcinkiewicz Integrals ◽  
Decomposition Theory ◽  
Logarithmic Type ◽  
Lipschitz Conditions

In this paper, by using the atomic decomposition theory of Hardy space H1(ℝn) and weak Hardy space WH1(ℝn), we give the boundedness properties of some operators with variable kernels such as singular integral operators, fractional integrals and parametric Marcinkiewicz integrals on these spaces, under certain logarithmic type Lipschitz conditions assumed on the variable kernel Ω(x, z).

scholarly journals Hardy spaces estimates for multilinear operators with homogeneous kernels

2003 ◽  
Vol 170 ◽  
pp. 117-133 ◽  
Author(s):  
Yong Ding ◽  
Shanzhen Lu
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Fractional Integral ◽  
Integral Operators ◽  
Kernel Functions ◽  
Multilinear Operators ◽  
Product Spaces ◽  
Bounded Operators ◽  
Fractional Integral Operators ◽  
Bmo Function

AbstractIn this paper the authors prove that a class of multilinear operators formed by the singular integral or fractional integral operators with homogeneous kernels are bounded operators from the product spaces Lp1 × Lp2 × · · · × LpK (ℝn) to the Hardy spaces Hq (ℝn) and the weak Hardy space Hq,∞(ℝn), where the kernel functions Ωij satisfy only the Ls-Dini conditions. As an application of this result, we obtain the (Lp, Lq) boundedness for a class of commutator of the fractional integral with homogeneous kernels and BMO function.

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).

H1 boundedness of oscillatory singular integrals with degenerate phase functions

1994 ◽  
Vol 116 (2) ◽  
pp. 353-358
Author(s):  
Yibiao Pan
Keyword(s):  
Hardy Space ◽  
Singular Integral ◽  
Phase Function ◽  
Infinite Order ◽  
Singular Integrals ◽  
Integral Operators ◽  
Uniform Boundedness ◽  
Sufficient Condition ◽  
Oscillatory Singular Integrals ◽  
Phase Functions

AbstractIn this paper we study the uniform boundedness of oscillatory singular integral operators with degenerate phase functions on the Hardy space H1. The H1 boundedness was previously known when the phase function is nondegenerate. Here we obtain a sufficient condition for H1 boundedness which allows the phase function vanishing to infinite order.

Certain Operators with Rough Singular Kernels

2003 ◽  
Vol 55 (3) ◽  
pp. 504-532 ◽  
Author(s):  
Jiecheng Chen ◽  
Dashan Fan ◽  
Yiming Ying
Keyword(s):  
Hardy Space ◽  
Sobolev Space ◽  
Singular Integral ◽  
Hardy Spaces ◽  
Integrable Function ◽  
Bounded Function ◽  
Bounded Operator ◽  
Integral Operators ◽  
Test Functions ◽  
Singular Kernels

AbstractWe study the singular integral operatordefined on all test functions f, where b is a bounded function, α ≥ 0, Ω (yʻ) is an integrable function on the unit sphere Sn-1 satisfying certain cancellation conditions. We prove that, for 1 < p < ∞, TΩ,α extends to a bounded operator from the Sobolev space to the Lebesgue space Lp with Ω being a distribution in the Hardy space Hq(Sn-1) where . The result extends some known results on the singular integral operators. As applications, we obtain the boundedness for TΩ,α on the Hardy spaces, as well as the boundedness for the truncated maximal operator .

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