Under which conditions is the Jacobi space $$L_{w^{(a,b)} }^p [ - 1,1]$$ subset of $$L_{w^{(\alpha ,\beta )} }^1 [ - 1,1]$$ ?

• Autorzy: Michael Felten
• Języki publikacji: EN

Abstrakty

EN

Exact conditions for α, β, a, b > −1 and 1 ≤ p ≤ ∞ are determined under which the inclusion property $$L_{w^{(a,b)} }^p [ - 1,1]$$ ⊂ $$L_{w^{(\alpha ,\beta )} }^1 [ - 1,1]$$ is valid. It is shown that the conditions characterize the inclusion property. The paper concludes with some results, in which the inclusion property can be detected in relation with estimates of Jacobi differential operators and with Muckenhoupt’s transplantation theorems and multiplier theorems for Jacobi series.

Słowa kluczowe

EN

Jacobi Spaces; Fourier expansion; Jacobi differential operators; transplantation theorems; multiplier theorems

Kategorie tematyczne

• 41A10: Approximation by polynomials
• 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2007
• Tom: 5
• Numer: 3
• Strony: 505-511

Daty

wydano

2007-09-01

online

2007-04-28

Twórcy

autor

Michael Felten

• Faculty of Mathematics and Informatics University of Hagen

Bibliografia

• [1] F. Dai and Z. Ditzian: “Littlewood-Paley theory and a sharp Marchaud inequality”, Acta Sci. Math. (Szeged), Vol. 71, (2005), pp. 65–90.
• [2] M. Felten: “Most of the First Order Jacobi K-Functionals are Equivalent”, submitted, pp. 1–12.
• [3] B. Muckenhoupt: “Mean convergence of Jacobi series”, Proc. Amer. Math. Soc., Vol. 23, (1969), pp. 306–310. http://dx.doi.org/10.2307/2037162
• [4] B. Muckenhoupt: “Transplantation theorems and multiplier theorems for Jacobi series”, Mem. Amer. Math. Soc., Vol. 64, (1986), pp. iv–86.

Identyfikatory

DOI

10.2478/s11533-007-0011-7