lp,q-bounded sequences in function spaces

Abstract

A sequence of measurable functions {fn} is called lp,q-bounded sequence, 0<p<∞,  0<q≤∞, if for any sequence of real numbers a={αn}∈lp,q we have sup⁡n⁡|αnFn(ω)|<∞  ω-a.e., for any sequence {Fn} such that for every n functions fn anf Fn are equimeasurable. The main result gives necessary and sufficient conditions for the sequence being lp,q-bounded.