MAXIMAL OPERATOR ON ORLICZ SPACES OF TWO VARIABLE EXPONENTS OVER UNBOUNDED QUASI-METRIC MEASURE SPACES.

In this paper, we are concerned with the boundedness of the Hardy-Littlewood maximal operator on the Orlicz space Lp(·)(log L)q(·)(X) of two variable exponents over unbounded quasi-metric measure spaces, as an extension of [Math Scand. 116 (2015), pp. 5–22]. The result is new even for the variable exponent Lebesgue space Lp(·)(X) in that the underlying spaces need not be bounded and that the underlying measure need not be doubling. [ABSTRACT FROM AUTHOR]