EXPONENTIAL INTEGRABILITY FOR LOGARITHMIC POTENTIALS OF FUNCTIONS IN GENERALIZED LEBESGUE SPACES $L(\log L)^{q(\cdot)}$ OVER NON-DOUBLING MEASURE SPACES

Abstract

In this paper, we are concerned with exponential integrability for logarithmic potentials of functions in generalized Lebesgue spaces $L(\log L)^{q(\cdot)}$ over non-doubling measure spaces. Here $q$ satisfies the loglog-Holder condition.