Hardy spaces generated by an integrability condition

DOI10.1006/jath.2001.3614zbMath0996.42003OpenAlexW1985467136MaRDI QIDQ5959023

Sandor Fridli

Publication date: 3 November 2002

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jath.2001.3614

zbMATH Keywords

Fourier transformWalsh systemHilbert transformintegrability conditionHardy spacesatoms

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Convergence and absolute convergence of Fourier and trigonometric series (42A20) Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) (42A32)

Related Items (25)

Integrability spaces for the Fourier transform of a function of bounded variation ⋮ Asymptotic Behavior of the Fourier Transform of a Function of Bounded Variation ⋮ A multiplier theorem for the Hankel transform on the associated Hardy space ⋮ Characterization of Banach valued BMO functions and UMD Banach spaces by using Bessel convolutions ⋮ Fourier transforms on an amalgam type space ⋮ \(L^p\) simulation for measures ⋮ Conditions for the absolute convergence of Fourier integrals ⋮ Fourier transform versus Hilbert transform ⋮ On the integrability of dyadic maximal Walsh series ⋮ On integrability and strong summability of Walsh-Kaczmarz series ⋮ Characterizations of the Hardy space 𝐻¹(ℝ) and BMO(ℝ) ⋮ BMO functions and balayage of Carleson measures in the Bessel setting ⋮ Fourier transforms on weighted amalgam-type spaces ⋮ Asymptotics of the Fourier sine transform of a function of bounded variation ⋮ The Fourier transform of a function of bounded variation: symmetry and asymmetry ⋮ Wiener algebras and trigonometric series in a coordinated fashion ⋮ The Wiener algebra of absolutely convergent Fourier integrals: an overview ⋮ The fractional Bessel equation in Hölder spaces ⋮ UMD-valued square functions associated with Bessel operators in Hardy and BMO spaces ⋮ Odd BMO\({(\mathbb{R})}\) functions and Carleson measures in the Bessel setting ⋮ Boundedness of Hausdorff operators on Hardy spaces in the Heisenberg group ⋮ Walsh Multipliers for Dyadic Hardy Spaces ⋮ Product Hardy, BMO spaces and iterated commutators associated with Bessel Schrodinger operators ⋮ On Hardy spaces associated with Bessel operators ⋮ Maximal operators, Riesz transforms and Littlewood-Paley functions associated with Bessel operators on BMO

Cites Work

• On asymptotics of Fourier transform for functions of certain classes
• Sidon-type inequalities for Legendre polynomials
• An inverse Sidon type inequality for the Walsh system
• Extensions of Hardy spaces and their use in analysis
• Integrability theorems for trigonometric series
• An inverse Sidon type inequality
• A real variable characterization of $H^{p}$
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