Abstract

The aim of this paper is to present sufficient and necessary conditions for generalized Hölder's inequality in Morrey spaces and generalized Morrey spaces. We also obtain similar results in weak Morrey spaces and generalized weak Morrey spaces. The sufficient and necessary conditions for the generalized Hölder's inequality in these spaces are obtained through estimates for characteristic functions of balls in $R^d$.

Keywords: Hölder's inequality; generalized Hölder's inequality; Morrey spaces; weak Morrey spaces; generalized Morrey spaces; generalized weak Morrey spaces.

MSC: 26D15, 46B25, 46E30

Pages:  326$-$337     

Volume  70 ,  Issue  4 ,  2018