Holder’s inequality in Discrete Morrey spaces

Abstract

Morrey spaces are a generalization of Lebesgue's spaces. There are two categories of Morrey spaces, i.e. continuous Morrey spaces and discrete Morrey spaces. Many authors have discussed about continuous Morrey spaces. In this paper, first we review definitions of these types, and then we present sufficient condition for Hlder's inequality in discrete Morrey spaces and in weak discrete Morrey spaces. One of the keys to prove our results is to use the Hlder's sequence of the balls in ℤ .

Inner Products on Discrete Morrey Spaces

“…Many mathematicians had discussed about the discrete Morrey space (see [1], [2], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [20], [21], and [22]). We have known that the space (m u,p , ∥ • ∥ mu,p ) is a normed space.…”