scholarly journals Dual spaces of dyadic Hardy spaces generated by a rearrangement invariant space X on [0,1]

1998 ◽  
Vol 36 (1) ◽  
pp. 163-175
Author(s):  
Nicolae Popa
Keyword(s):  
Hardy Spaces ◽  
Rearrangement Invariant Space ◽  
Invariant Space ◽  
Dual Spaces

On dual spaces of anisotropic Hardy spaces

2012 ◽  
Vol 285 (17-18) ◽  
pp. 2078-2092 ◽  
Author(s):  
Shai Dekel ◽  
Tal Weissblat
Keyword(s):  
Hardy Spaces ◽  
Dual Spaces

scholarly journals Multiplication between Hardy spaces and their dual spaces

2019 ◽  
Vol 131 ◽  
pp. 130-170 ◽  
Author(s):  
Aline Bonami ◽  
Jun Cao ◽  
Luong Dang Ky ◽  
Liguang Liu ◽  
Dachun Yang ◽  
...  
Keyword(s):  
Hardy Spaces ◽  
Dual Spaces

Variable exponents and grand Lebesgue spaces: Some optimal results

2015 ◽  
Vol 17 (06) ◽  
pp. 1550023 ◽  
Author(s):  
Alberto Fiorenza ◽  
Jean Michel Rakotoson ◽  
Carlo Sbordone
Keyword(s):  
Variable Exponent ◽  
Bounded Function ◽  
Rearrangement Invariant Space ◽  
Invariant Space ◽  
Lebesgue Spaces ◽  
Bounded Set ◽  
Decreasing Rearrangement ◽  
Grand Lebesgue Spaces ◽  
Measurable Bounded Function ◽  
Grand Lebesgue Space

Consider p : Ω → [1, +∞[, a measurable bounded function on a bounded set Ø with decreasing rearrangement p* : [0, |Ω|] → [1, +∞[. We construct a rearrangement invariant space with variable exponent p* denoted by [Formula: see text]. According to the growth of p*, we compare this space to the Lebesgue spaces or grand Lebesgue spaces. In particular, if p*(⋅) satisfies the log-Hölder continuity at zero, then it is contained in the grand Lebesgue space Lp*(0))(Ω). This inclusion fails to be true if we impose a slower growth as [Formula: see text] at zero. Some other results are discussed.

scholarly journals Dual spaces of anisotropic mixed-norm Hardy spaces

2018 ◽  
Vol 147 (3) ◽  
pp. 1201-1215 ◽  
Author(s):  
Long Huang ◽  
Jun Liu ◽  
Dachun Yang ◽  
Wen Yuan
Keyword(s):  
Hardy Spaces ◽  
Mixed Norm ◽  
Dual Spaces

Extrapolation of Lp Data from a Modular Inequality

2002 ◽  
Vol 45 (1) ◽  
pp. 25-35
Author(s):  
Steven Bloom ◽  
Ron Kerman
Keyword(s):  
Orlicz Spaces ◽  
Rearrangement Invariant Space ◽  
Invariant Space ◽  
Partial Converse

AbstractIf an operator T satisfies a modular inequality on a rearrangement invariant space Lρ(Ω, μ), and if p is strictly between the indices of the space, then the Lebesgue inequality holds. This extrapolation result is a partial converse to the usual interpolation results. A modular inequality for Orlicz spaces takes the form , and here, one can extrapolate to the (finite) indices i(Φ) and I(Φ) aswell.

scholarly journals Dual Spaces of Multiparameter Local Hardy Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Wei Ding ◽  
Feng Yu
Keyword(s):  
Hardy Spaces ◽  
Duality Theory ◽  
Carleson Measure ◽  
Dual Spaces ◽  
Local Hardy Spaces ◽  
The Relationship

In this paper, we study the duality theory of the multiparameter local Hardy spaces h p ℝ n 1 × ℝ n 2 , and we prove that h p ℝ n 1 × ℝ n 2 ∗ = cm o p ℝ n 1 × ℝ n 2 , where cm o p ℝ n 1 × ℝ n 2 are defined by discrete Carleson measure. Moreover, we discuss the relationship among cm o p ℝ n 1 × ℝ n 2 , Li p p ℝ n 1 × ℝ n 2 , and rectangle cm o rect p ℝ n 1 × ℝ n 2 .

Convolution in Weighted Lorentz Spaces of Type $\Gamma$

2016 ◽  
Vol 119 (1) ◽  
pp. 113 ◽  
Author(s):  
Martin Křepela
Keyword(s):  
Convolution Operator ◽  
Lorentz Spaces ◽  
Rearrangement Invariant Space ◽  
Invariant Space ◽  
Weighted Lorentz Spaces

We characterize boundedness of the convolution operator between weighted Lorentz spaces $\Gamma^p(v)$ and $\Gamma^q(w)$ for the range of parameters $p,q\in[1,\infty]$, or $p\in(0,1)$ and $q\in\{1,\infty\}$, or $p=\infty$ and $q\in(0,1)$. We provide Young-type convolution inequalities of the form \[ \|f\ast g\|_{\Gamma^q(w)} \le C \|f\|_{\Gamma^p(v)}\|g\|_Y, \quad f\in\Gamma^p(v), g\in Y, \] characterizing the optimal rearrangement-invariant space $Y$ for which the inequality is satisfied.

Weighted Carleson Measure Spaces Associated with Different Homogeneities

2014 ◽  
Vol 66 (6) ◽  
pp. 1382-1412 ◽  
Author(s):  
Xinfeng Wu
Keyword(s):  
Hardy Spaces ◽  
Carleson Measure ◽  
Forthcoming Paper ◽  
Weighted Hardy Spaces ◽  
Dual Spaces ◽  
Measure Spaces

AbstractIn this paper, we introduce weighted Carleson measure spaces associated with different homogeneities and prove that these spaces are the dual spaces of weighted Hardy spaces studied in a forthcoming paper. As an application, we establish the boundedness of composition of two Calderón–Zygmund operators with different homogeneities on the weighted Carleson measure spaces; this, in particular, provides the weighted endpoint estimates for the operators studied by Phong–Stein.

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