Extrapolation Theorem on Some Quasi-Banach Spaces

Abstract

In [5], the author has proved extended sharp extrapolation theorem on $L^p$ spaces with $\sum$-method ([1]), which asserted $\sum_{1<p<q}((p-1)^{-\alpha}L^p)^{p/q}=(L\log^{\alpha}L+L^q)^{1/q}$. In the present paper, on that result, we shall consider the case $q\approx 1$.