Statistics requires consideration of the “ideal estimates” defined through the posterior mean of fractional powers of finite measures. In this paper we study L1= , the linear space spanned by th power of finite measures, 2 (0; 1). It is shown that L1= generalizes the Lebesgue function space L1= ( ), and shares most of its important properties: It is a uniformly convex (hence reflexive) Banach s...

We study a natural question that, apparently, has not been well addressed in the literature. Given functions u with support unit ball B 1 ? R n and gradient Morrey space M p , ? ( ) where < what is largest range of exponents q for which necessarily ? L ? While David R. Adams proved 1975 that this embedding holds ? / ? an article from 2011 claimed larger . Here we disprove last statement by cons...

We study Lebesgue and Atsuji spaces within subsystems of second order arithmetic. The former spaces are those such that every open covering has a Lebesgue number, while the latter are those such that every continuous function defined on them is uniformly continuous. The main results we obtain are the following: the statement “every compact space is Lebesgue” is equivalent to WKL0; the statement...

In this paper, we introduce and analyze several different notions of Weyl almost periodic functions ergodic components in Lebesgue spaces with variable exponent Lp(x). We investigate the invariance (asymptotical) periodicity under actions convolution products, providing also some illustrative applications to abstract fractional differential inclusions Banach spaces. The introduced classes gener...