The Littlewood-Paley Theory for Jacobi Expansions

DOI10.2307/1998690zbMath0468.42010OpenAlexW4239226072MaRDI QIDQ3921642

William C. Connett, Alan L. Schwartz

Publication date: 1979

Full work available at URL: https://doi.org/10.2307/1998690

zbMATH Keywords

maximal functionsconvolution kernelmultiplier theoremsJacobi polynomial expansionsLittlewood-Paley functionals

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Multipliers in one variable harmonic analysis (42A45)

Related Items (18)

A Hardy-Littlewood Maximal Inequality for Jacobi Type Hypergroups ⋮ The Hardy-Littlewood-Sobolev theorem for Riesz potential generated by Gegenbauer operator ⋮ Maximal function on the dual of Laguerre hypergroup ⋮ Product formulas, hypergroups, and the Jacobi polynomials ⋮ Unnamed Item ⋮ Maximal functions for Weinstein operator ⋮ Characterizations of smoothness of functions in terms of their Jacobi expansions ⋮ On the boundedness of fractional maximal and Riesz potential operators associated with Kontorovich–Lebedev transform ⋮ Hardy spaces for Dunkl-Gegenbauer expansions ⋮ Dunkl translation and uncentered maximal operator on the real line ⋮ Unnamed Item ⋮ On fractional maximal function and fractional integral on the Laguerre hypergroup ⋮ Analysis of a Class of Probability Preserving Measure Algebras on Compact Intervals ⋮ Characterizations of smoothness of functions in terms of the basis conjugate to Jacobi polynomials ⋮ Summability of product Jacobi expansions ⋮ Boundedness of integral operators associated with the Kontorovich–Lebedev transform in the Lebesgue spaces type ⋮ Analysis related to all admissible type parameters in the Jacobi setting ⋮ Weighted estimates of singular integrals and their applications

Cites Work

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• The mean convergence of orthogonal series. III
• A characterization of localized Bessel potential spaces and applications to Jacobi and Henkel multipliers
• A multiplier theorem for ultraspherical series
• The theory of ultraspherical multipliers
• Multiplier Criteria of Marcinkiewicz Type for Jacobi Expansions
• Sommes De Cesaro Et Multiplicateurs Des Developpements en Harmoniques Spheriques
• Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63)
• Jacobi Polynomials, II. An Analytic Proof of the Product Formula
• A multiplier theorem for Jacobi expansions

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