L p -Boundedness of Marcinkiewicz Integrals with Hardy Space Function Kernels

2000 ◽  
Vol 16 (4) ◽  
pp. 593-600 ◽  
Author(s):  
Yong Ding ◽  
Dashan Fan ◽  
Yibiao Pan
Keyword(s):  
Hardy Space ◽  
Marcinkiewicz Integrals ◽  
Space Function

L p -Boundedness of Marcinkiewicz Integrals with Hardy Space Function Kernels

2000 ◽  
Vol 16 (4) ◽  
pp. 593-600 ◽  
Author(s):  
Yong Ding ◽  
Dashan Fan ◽  
Yibiao Pan
Keyword(s):  
Hardy Space ◽  
Marcinkiewicz Integrals ◽  
Space Function

scholarly journals Marcinkiewicz Integrals on Weighted Weak Hardy Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yue Hu ◽  
Yueshan Wang
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Lebesgue Space ◽  
Muckenhoupt Weight ◽  
Marcinkiewicz Integral ◽  
Smoothness Condition ◽  
Weight Class ◽  
Marcinkiewicz Integrals ◽  
Weak Hardy Space ◽  
Weak Lebesgue Space

We prove that, under the conditionΩ∈Lipα, Marcinkiewicz integralμΩis bounded from weighted weak Hardy spaceWHwpRnto weighted weak Lebesgue spaceWLwpRnformaxn/n+1/2,n/n+α<p≤1, wherewbelongs to the Muckenhoupt weight class. We also give weaker smoothness condition assumed on Ω to imply the boundedness ofμΩfromWHw1ℝntoWLw1Rn.

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 Marcinkiewicz integrals with variable kernels on Hardy and weak Hardy spaces

2010 ◽  
Vol 8 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Xiangxing Tao ◽  
Xiao Yu ◽  
Songyan Zhang
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Marcinkiewicz Integrals ◽  
Dini Condition ◽  
Weak Hardy Space

In this article, we consider the Marcinkiewicz integrals with variable kernels defined byμΩ(f)(x)=(∫0∞|∫|x−y|≤tΩ(x,x−y)|x−y|n−1f(y)dy|2dtt3)1/2, whereΩ(x,z)∈L∞(ℝn)×Lq(Sn−1)forq> 1. We prove that the operatorμΩis bounded from Hardy space,Hp(ℝn), toLp(ℝn)space; and is bounded from weak Hardy space,Hp,∞(ℝn), to weakLp(ℝn)space formax{2n2n+1,nn+α}<p<1, ifΩsatisfies theL1,α-Dini condition with any0<α≤1.

Noncommutative Function-Theoretic Operator Theory and Applications

2021 ◽  
Author(s):  
Joseph A. Ball ◽  
Vladimir Bolotnikov
Keyword(s):  
System Theory ◽  
Hardy Space ◽  
Operator Theory ◽  
Reproducing Kernel ◽  
Invariant Subspaces ◽  
Weighted Bergman Space ◽  
Characteristic Operator ◽  
Multivariable Operator Theory ◽  
Backward Shift ◽  
Space Function

This concise monograph explores how core ideas in Hardy space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system theory ideas and reproducing kernel techniques, the book then covers representations of backward-shift-invariant subspaces in the Hardy space as ranges of observability operators, and representations for forward-shift-invariant subspaces via a Beurling–Lax representer equal to the transfer function of the linear system. This pair of backward-shift-invariant and forward-shift-invariant subspace form a generalized orthogonal decomposition of the ambient Hardy space. All this leads to the de Branges–Rovnyak model theory and characteristic operator function for a Hilbert space contraction operator. The chapters that follow generalize the system theory and reproducing kernel techniques to enable an extension of the ideas above to weighted Bergman space multivariable settings.

Extracting outer function part from Hardy space function

2017 ◽  
Vol 60 (11) ◽  
pp. 2321-2336 ◽  
Author(s):  
LiHui Tan ◽  
Tao Qian
Keyword(s):  
Hardy Space ◽  
Outer Function ◽  
Space Function

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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