On some approximation properties of real Hardy spaces \((0<p\leq 1)\)
type: Item
instance of: scholarly article
title: On some approximation properties of real Hardy spaces \((0<p\leq 1)\)
zbMATH Open document ID: 0577.41021
DOI: 10.1016/0021-9045(84)90134-5
published in: Journal of Approximation Theory
publication date: 1984-01-01T00:00:00Z
review text: In the real Hardy spaces Re \(H_ p\) defined on the one-dimensional torus T or on \({\mathbb{R}}\), \(0<p\leq 1\), the author proves some analogous inequalities of approximation theory known for \(L_ p(T)\), \(1\leq p<\infty\), using atomic decompositions and molecules. One can find e.g., a description of the Re \(H_ p\)-moduli of continuity by a corresponding K'-functional, a Jackson-type inequality for the approximation of u(t)\(\in Re H_ p(T)\) by the partial sums \(P^ m_ nu(t)\) of its Fourier series with respect to the periodic orthonormal spline systems \(F^{(m)}\) \((m=1,2,...)\) introduced by Z. Ciesielski and the approximation by Bochner-Riesz means of the Fourier integral of distributions belonging to Re \(H_ p({\mathbb{R}})\).
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 42A24
zbMATH DE Number: 3923340
zbMATH Keywords: real Hardy spaces
zbMATH Keywords: atomic decompositions
zbMATH Keywords: molecules
zbMATH Keywords: Bochner-Riesz means
zbMATH Keywords: Fourier integral of distributions
author: Peter Oswald
MaRDI profile type: Publication
full work available at URL: 0021-9045(84)90134-5
OpenAlex ID: W1988924525
cites work: Q4112938
cites work: Q4863278
cites work: Constructive function theory and spline systems
cites work: Construction of an orthonormal basis in $C^{m}(I^{d})$ and $W^{m}_{p}(I^{d})$
cites work: A real variable characterization of $H^{p}$
cites work: Extensions of Hardy spaces and their use in analysis
cites work: Q4143683
cites work: Q5618011
cites work: \(H^p\) spaces of several variables
cites work: Q5669012
cites work: Russian text ignoredLp, 0 <p < 1
cites work: On Schauder bases in Hardy spaces
cites work: On spline bases in periodic Hardy spaces (0 <p  1)
cites work: Q5546246
cites work: Convolution with Oscillating Kernels on H P Spaces
cites work: Q5640160
cites work: Q3969347
cites work: Q4165580
cites work: Q4165579
cites work: Q4165578
cites work: Q4387439
cites work: Q3903472
cites work: DIRECT AND CONVERSE THEOREMS OF JACKSON TYPE IN $ L^p$ SPACES, $ 0<p<1$
cites work: Q4195422
cites work: Q4740809
cites work: $H_{p}$-spaces, p≤1, and spline systems
cites work: Q4039793
Recommended article: Q3764641
Recommended article: Q3485394
Recommended article: Q3812713
Recommended article: Hardy approximation to \(L^p\) functions on subsets of the circle with \(1\leq p<\infty\)
Recommended article: Approximation properties of generalized Bochner-Riesz means in the Hardy spaces $ H_p$, $ 0<p\le 1$
Recommended article: Q3582580
Recommended article: Approximation in Hardy spaces
Recommended article: On a rational approximation problem in the real Hardy space \(H_ 2\)
Recommended article: Hardy space decompositions of Lp(ℝn) for 0 < p < 1 with rational approximation
Recommended article: Q4326038
description: scientific article; zbMATH DE number 3923340