An Anisotropic Approach To Mid Summable Sequences

The purpose of this paper is to present an anisotropic theory for mid summable sequences by defining a more general space, called the space of mid (q,p)-summable sequences. As a particular case of our results, we prove an inclusion relation between spaces of mid summable sequences. We also define a class of operators acting on this new space, the mid (q,p)-summing operators, and prove some inclusion and coincidence results and a Pietsch domination-type theorem. It is worth mentioning that the above results are new even in the particular case of mid p-summable sequences.