𝐿^{𝑝} norms of certain kernels of the 𝑁-dimensional torus

Colzani, L.; Soardi, P. M.

doi:10.1090/S0002-9947-1981-0617555-7

$L^{p}$ norms of certain kernels of the $N$-dimensional torus
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by L. Colzani and P. M. Soardi PDF

Trans. Amer. Math. Soc. 266 (1981), 617-627 Request permission

Abstract:

In this paper we study a class of kernels ${F_R}$ which generalize the Bochner-Riesz kernels on the $N$-dimensional torus. Our main result consists in upper estimates for the ${L^p}$ norms of ${F_R}$ 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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