Weak factorization of the Hardy space H for small values of p, in the multilinear setting

2020 ◽  
Vol 485 (1) ◽  
pp. 123711
Author(s):  
Marie-José S. Kuffner
Keyword(s):  
Hardy Space ◽  
Weak Factorization

scholarly journals A note on weak factorization of a Meyer-type Hardy space via a Cauchy integral operator

2020 ◽  
Vol 253 (3) ◽  
pp. 307-327
Author(s):  
Yongsheng Han ◽  
Ji Li ◽  
Cristina Pereyra ◽  
Brett D. Wick
Keyword(s):  
Hardy Space ◽  
Integral Operator ◽  
Cauchy Integral ◽  
Weak Factorization

scholarly journals Weak Factorizations of the Hardy Space H1(ℝn) in Terms of Multilinear Riesz Transforms

2017 ◽  
Vol 60 (3) ◽  
pp. 571-585 ◽  
Author(s):  
Ji Li ◽  
Brett D. Wick
Keyword(s):  
Hardy Space ◽  
Direct Application ◽  
Riesz Transforms ◽  
Constructive Proof ◽  
Weak Factorization ◽  
Classical Hardy Space

AbstractThis paper provides a constructive proof of the weak factorization of the classical Hardy space H1(ℝn) in terms of multilinear Riesz transforms. As a direct application, we obtain a new proof of the characterization of BMO(ℝn) (the dual of H1(ℝn)) via commutators of the multilinear Riesz transforms.

Boundedness and compactness characterizations of Riesz transform commutators on Morrey spaces in the Bessel setting

2018 ◽  
Vol 17 (01) ◽  
pp. 145-178 ◽  
Author(s):  
Suzhen Mao ◽  
Huoxiong Wu ◽  
Dongyong Yang
Keyword(s):  
Hardy Space ◽  
Riesz Transform ◽  
Morrey Spaces ◽  
Bessel Operator ◽  
Factorization Theorem ◽  
Commutator Formula ◽  
Weak Factorization

Let [Formula: see text] and [Formula: see text] be the Bessel operator on [Formula: see text]. In this paper, the authors show that [Formula: see text] (or [Formula: see text], respectively) if and only if the Riesz transform commutator [Formula: see text] is bounded (or compact, respectively) on Morrey spaces [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text]. A weak factorization theorem for functions belonging to the Hardy space [Formula: see text] in the sense of Coifman–Rochberg–Weiss in Bessel setting, via [Formula: see text] and its adjoint, is also obtained.

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 ).

The range of block Hankel operators

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3237-3243
Author(s):  
In Hwang ◽  
In Kim ◽  
Sumin Kim
Keyword(s):  
Hardy Space ◽  
Invariant Subspace ◽  
Hankel Operators ◽  
Coprime Factorization ◽  
Backward Shift ◽  
Vector Valued

In this note we give a connection between the closure of the range of block Hankel operators acting on the vector-valued Hardy space H2Cn and the left coprime factorization of its symbol. Given a subset F ? H2Cn, we also consider the smallest invariant subspace S*F of the backward shift S* that contains F.

Interpolation on weak martingale Hardy space

2009 ◽  
Vol 25 (8) ◽  
pp. 1297-1304 ◽  
Author(s):  
Yong Jiao ◽  
Wei Chen ◽  
Pei De Liu
Keyword(s):  
Hardy Space ◽  
Martingale Hardy Space

ANALYTIC SAMPLING APPROXIMATION BY PROJECTION OPERATOR WITH APPLICATION IN DECOMPOSITION OF INSTANTANEOUS FREQUENCY

2013 ◽  
Vol 11 (05) ◽  
pp. 1350040 ◽  
Author(s):  
YOUFA LI ◽  
TAO QIAN
Keyword(s):  
Hardy Space ◽  
Numerical Experiment ◽  
Hilbert Transform ◽  
Mild Condition ◽  
Instantaneous Frequency ◽  
Projection Operator ◽  
Approximation Scheme ◽  
Special Functions ◽  
Cauchy Kernel ◽  
Sequence Of Functions

A sequence of special functions in Hardy space [Formula: see text] are constructed from Cauchy kernel on unit disk 𝔻. Applying projection operator of the sequence of functions leads to an analytic sampling approximation to f, any given function in [Formula: see text]. That is, f can be approximated by its analytic samples in 𝔻s. Under a mild condition, f is approximated exponentially by its analytic samples. By the analytic sampling approximation, a signal in [Formula: see text] can be approximately decomposed into components of positive instantaneous frequency. Using circular Hilbert transform, we apply the approximation scheme in [Formula: see text] to Ls(𝕋2) such that a signal in Ls(𝕋2) can be approximated by its analytic samples on ℂs. A numerical experiment is carried out to illustrate our results.

New variable martingale Hardy spaces

2021 ◽  
pp. 1-29
Author(s):  
Yong Jiao ◽  
Dan Zeng ◽  
Dejian Zhou
Keyword(s):  
Brownian Motion ◽  
Hardy Space ◽  
Hardy Spaces ◽  
Stochastic Integral ◽  
Lebesgue Spaces ◽  
Type Space ◽  
Variable Lebesgue Spaces ◽  
Martingale Inequalities

We investigate various variable martingale Hardy spaces corresponding to variable Lebesgue spaces $\mathcal {L}_{p(\cdot )}$ defined by rearrangement functions. In particular, we show that the dual of martingale variable Hardy space $\mathcal {H}_{p(\cdot )}^{s}$ with $0<p_{-}\leq p_{+}\leq 1$ can be described as a BMO-type space and establish martingale inequalities among these martingale Hardy spaces. Furthermore, we give an application of martingale inequalities in stochastic integral with Brownian motion.

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