Yoshihiro Sawano

Generalized fractional integral operators and fractional maximal operators in the framework of Morrey spaces

The action of the generalized fractional integral operators and the generalized fractional maximal operators is investigated in the framework of Morrey spaces. A typical property of the functions which belongs to Morrey spaces under pointwise multiplication by the generalized fractional integral operators and the generalized fractional maximal operators is established. The boundedness property of the fractional integral operators on the predual of Morrey spaces is shown as well. A counterexample concerning the FeffermanPhong inequality is given by the use of the characteristic function of the Cantor set.

Limiting case of the boundedness of fractional integral operators on nonhomogeneous space

We show the boundedness of fractional integral operators by means of extrapolation. We also show that our result is sharp.

FRACTIONAL INTEGRAL OPERATORS IN NONHOMOGENEOUS SPACES

We shall here discuss the boundedness of the fractional integral operator Iα and its generalized version on generalized non-homogeneous Morrey spaces. To prove the boundedness of Iα, we employ the boundedness of the so-called maximal fractional integral operator I∗ a,κ. In addition, we prove an Olsen-type inequality, which is analogous to that in the case of homogeneous type.

Uniqueness criterion of weak solutions for the dissipative quasi-geostrophic equations in Orlicz–Morrey spaces

Consider the quasi-geostrophic equations with the initial data . Let and be two weak solutions with the same initial value . If where is the Orlicz–Morrey space (for a definition of this space, see Definition ), then we have . In view of the embedding with and , we see that our result improves the previous result of Dong and Chen. This is an extension of earlier regularity results in the Serrin’s type space .

A Note on Generalized Fractional Integral Operators on Generalized Morrey Spaces

We show some inequalities for generalized fractional integral operators on generalized Morrey spaces. We also show the boundedness property of the generalized fractional integral operators on the predual of the generalized Morrey spaces.

Discrete linear differential equations

Abstract We propose new constructions of the approximate solutions of discrete linear differential equations and their inverse source problems. This is mainly based on a reproducing kernel Hilbert spaces approach where different types of spaces are naturally considered as a consequence of the method. Here, the major influence will be given by the Paley–Wiener and Sobolev spaces.

A remark on two generalized Orlicz-Morrey spaces

There have been known two generalized Orlicz-Morrey spaces. One is defined earlier by Nakai and the other is by Sugano, the second and third authors. In this paper we investigate differences between these two spaces in some typical cases. The arguments rely upon property of the characteristic function of the Cantor set.

Sobolev’s inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces

Our aim in this paper is to give Sobolev’s inequality for Riesz potentials of functions in generalized Morrey spaces with variable exponent attaining the value 1 over non-doubling measure spaces. The main result is oriented to the outrange of the well-known Adams theorem.MSC: 31B15, 46E35, 26A33.

Pasting Reproducing Kernel Hilbert Spaces

The aim of this article is to find the necessary and sufficient condition for the mapping