Abstract For all admissible values of the numerical parameters sharp sufficient conditions on functional are obtained ensuring boundedness generalized Riesz potential from one general local Morrey-type space to another one, which, for a certain range parameters, coincide with necessary ones.

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...

The targets of this article are threefold. first one is to give a survey on the recent developments function spaces with mixed norms, including Lebesgue spaces, iterated weak mixed-norm and Morrey as well anisotropic Hardy spaces. second provide detailed proof for useful inequality about norms Hardy--Littlewood maximal operator also improve some known results characterizations boundedness Calde...

The �-dimensional Lebesgue space is the measurable space (E���(E�))— where E = [0 � 1) or E = R—endowed with the Lebesgue measure, and the “calculus of functions” on Lebesgue space is just “real and harmonic analysis.” The �-dimensional Gauss space is the same measure space (R���(R�)) as in the previous paragraph, but now we endow that space with the Gauss measure P� in place of the Lebesgue me...

In this paper, we give the necessary and sufficient conditions for boundedness of Hardy-Ces?ro operators on some weighted function spaces such as central Morrey, local non-local Herz Morrey-Herz type with variable exponent.

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...