In this paper we study a class of kernels FR which generalize the Bochner-Riesz kernels on the A-dimensional torus. Our main result consists in upper estimates for the Lp norms of FR as R tends to infinity. As a consequence we prove a convergence theorem for means of functions belonging to suitable Besov spaces
Colzani, L., Soardi, P. (1981). Lp norms of certain kernels on the tv-dimensional torus. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 266(2), 617-627 [10.1090/S0002-9947-1981-0617555-7].
Lp norms of certain kernels on the tv-dimensional torus
COLZANI, LEONARDO;SOARDI, PAOLO MAURIZIO
1981
Abstract
In this paper we study a class of kernels FR which generalize the Bochner-Riesz kernels on the A-dimensional torus. Our main result consists in upper estimates for the Lp norms of FR as R tends to infinity. As a consequence we prove a convergence theorem for means of functions belonging to suitable Besov spaces
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