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Transactions of the American Mathematical Society

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$ L\sp{p}$ norms of certain kernels of the $ N$-dimensional torus


Authors: L. Colzani and P. M. Soardi
Journal: Trans. Amer. Math. Soc. 266 (1981), 617-627
MSC: Primary 42A24; Secondary 46E30
DOI: https://doi.org/10.1090/S0002-9947-1981-0617555-7
MathSciNet review: 617555
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1981-0617555-7
Keywords: $ {L^p}$ norms, periodic functions, Bochner-Riesz kernels, Besov spaces, convergence of means, Lebesgue constants
Article copyright: © Copyright 1981 American Mathematical Society