Boundedness of Multilinear Operators in Herz-type Hardy Space

2000 ◽  
Vol 16 (2) ◽  
pp. 295-306
Author(s):  
Lin Tang ◽  
Dachun Yang
Keyword(s):  
Hardy Space ◽  
Multilinear Operators ◽  
Herz Type Hardy Space

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

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 The molecular characterization of anisotropic Herz-type Hardy spaces with two variable exponents

2020 ◽  
Vol 18 (1) ◽  
pp. 434-447
Author(s):  
Qingdong Guo ◽  
Wenhua Wang
Keyword(s):  
Hardy Space ◽  
Molecular Characterization ◽  
Hardy Spaces ◽  
Variable Exponents ◽  
Herz Type Hardy Space

Abstract In this article, the authors establish the characterizations of a class of anisotropic Herz-type Hardy spaces with two variable exponents associated with a non-isotropic dilation on {{\mathbb{R}}}^{n} in terms of molecular decompositions. Using the molecular decompositions, the authors obtain the boundedness of the central δ-Calderón-Zygmund operators on the anisotropic Herz-type Hardy space with two variable exponents.

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 Variable Herz estimates for fractional integral operators

2020 ◽  
Vol 72 (8) ◽  
pp. 1034-1046
Author(s):  
R. Heraiz
Keyword(s):  
Hardy Space ◽  
Fractional Integral ◽  
Atomic Decomposition ◽  
Integral Operators ◽  
Author Study ◽  
Fractional Integral Operators ◽  
Herz Type Hardy Space

UDC 517.5 In this paper, the author study the boundedness of fractional integral operators on a variable Herz-type Hardy space by using the atomic decomposition.

The maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series

2008 ◽  
Vol 45 (3) ◽  
pp. 321-331
Author(s):  
István Blahota ◽  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Hardy Space ◽  
Maximal Operator ◽  
Fejér Means

In this paper we prove that the maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series is not bounded from the Hardy space H2/3 ( G2 ) to the space L2/3 ( G2 ).

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