Notes on Fourier Analysis. (XXIX): An Extrapolation Theorem

Abstract

1. Introduction.Let $f(x)$ be a real measurable function defined in the interval $(0,2\pi)$ we write $f(x)\in L^{p}(p>0)$ when $|f(x)|^{p}$ is integrable in $(0,2\pi)$ , and $f(x)\in L^{*k}(a>0)$ when $\psi(x)|\log^{k}(1+f^{\wedge}(x))$ is integrable in $(0,2\pi)$ .$L^{*1}$ is the function class which was introduced by A. Zygmund [1].

Locations

• Journal of the Mathematical Society of Japan - View - PDF