Abstract
We study the modified Bessel -integral, whose properties are similar to those of the Bessel potential, and the modified Bessel - derivative. These operators are inverse to each other. We prove analogues of the embedding theorems of Hardy, Littlewood, Stein, Zygmund and Lizorkin concerning the images of under the action of Bessel potentials. We give applications of the Bessel integral and derivative to the integrability of the -adic Fourier transform and to approximation theory (an embedding theorem of Ul'yanov type).
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