Almost everywhere convergence of the inverse Jacobi transform and endpoint results for a disc multiplier

• Autorzy: Troels Roussau Johansen
• Języki publikacji: EN

Abstrakty

EN

The maximal operator S⁎ for the spherical summation operator (or disc multiplier) $S_{R}$ associated with the Jacobi transform through the defining relation $\widehat{S_{R}f}(λ) = 1_{|λ|≤R}f̂(t)$ for a function f on ℝ is shown to be bounded from $L^{p}(ℝ₊,dμ)$ into $L^{p}(ℝ,dμ) + L²(ℝ,dμ)$ for (4α + 4)/(2α + 3) < p ≤ 2. Moreover S⁎ is bounded from $L^{p₀,1}(ℝ₊,dμ)$ into $L^{p₀,∞}(ℝ,dμ) + L²(ℝ,dμ)$. In particular ${S_{R}f(t)}_{R>0}$ converges almost everywhere towards f, for $f ∈ L^{p}(ℝ₊,dμ)$, whenever (4α + 4)/(2α + 3) < p ≤ 2.

Kategorie tematyczne

• 43A50: Convergence of Fourier series and of inverse transforms
• 34E05: Asymptotic expansions
• 33C05: Classical hypergeometric functions, 2 F 1

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 205
• Numer: 2
• Strony: 101-137

Daty

wydano

2011

Twórcy

autor

Troels Roussau Johansen

• Mathematisches Seminar, Christian-Albrechts Universität zu Kiel, Ludewig-Meyn-Strasse 4, D-24098 Kiel, Germany

Identyfikatory

DOI

10.4064/sm205-2-1