Equiconvergence for Laguerre function series

• Autorzy: Krzysztof Stempak
• Języki publikacji: EN

Abstrakty

EN

We prove an equiconvergence theorem for Laguerre expansions with partial sums related to partial sums of the (non-modified) Hankel transform. Combined with an equiconvergence theorem recently proved by Colzani, Crespi, Travaglini and Vignati this gives, via the Carleson-Hunt theorem, a.e. convergence results for partial sums of Laguerre function expansions.

Słowa kluczowe

EN

equiconvergence; Laguerre series; Hankel transform

Kategorie tematyczne

• 42C99: None of the above, but in this section
• 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 118
• Numer: 3
• Strony: 285-300

Daty

wydano

1996

otrzymano

1995-10-16

poprawiono

1995-12-11

Twórcy

autor

Krzysztof Stempak

• Institute of Mathematics, Polish Academy of Sciences, Kopernika 18, 51-617 Wrocław, Poland

Bibliografia

• [CCTV] L. Colzani, A. Crespi, G. Travaglini and M. Vignati, Equiconvergence theorems for Fourier-Bessel expansions with applications to the harmonic analysis of radial functions in euclidean and noneuclidean spaces, Trans. Amer. Math. Soc. 338 (1993), 43-55.
• [Ma] C. Markett, Mean Cesàro summability of Laguerre expansions and norm estimates with shifted parameter, Anal. Math. 8 (1982), 19-37.
• [M1] B. Muckenhoupt, Mean convergence of Hermite and Laguerre series. II, Trans. Amer. Math. Soc. 147 (1970), 433-460.
• [M2] B. Muckenhoupt, Equiconvergence and almost everywhere convergence of Hermite and Laguerre series, SIAM J. Math. Anal. 1 (1970), 295-321.
• [St1] K. Stempak, On connections between Hankel, Laguerre and Heisenberg multipliers, J. London Math. Soc. 51 (1995), 286-298.
• [St2] K. Stempak, Transplanting maximal inequalities between Laguerre and Hankel multipliers, Monatsh. Math., to appear.
• [Sz] G. Szegö, Orthogonal Polynomials, Colloq. Publ. 23, Amer. Math. Soc., New York, 1939.