Takao Ohno

Riesz potentials and Sobolev embeddings on Morrey spaces of variable exponents

Let α, ν, β, p and q be variable exponents. Our aim in this article is to deal with Sobolev embeddings for Riesz potentials of order α with functions f in Morrey spaces L Φ,ν,β(G) with Φ(t) = t p (log(e + t)) q over a bounded open set G ⊂ R n . Here p and q satisfy the log-Hölder and the loglog-Hölder conditions, respectively. Also the case when p attains the value 1 in some parts of the domain is included in our results.

SOBOLEV INEQUALITIES FOR ORLICZ SPACES OF TWO VARIABLE EXPONENTS

Our aim in this paper is to deal with Sobolevs embeddings for Sobolev–Orlicz functions with ∇ u ∈ L p (·) log L q (·) (Ω) for Ω ⊂ n . Here p and q are variable exponents satisfying natural continuity conditions. Also the case when p attains the value 1 in some parts of the domain is included in the results.

Herz–Morrey spaces of variable exponent, Riesz potential operator and duality

Our aim in this paper is to deal with the boundedness of the Hardy–Littlewood maximal operator on Herz–Morrey spaces and to establish Sobolev’s inequalities for Riesz potentials of functions in Herz–Morrey spaces. Further, we discuss the associate spaces among Herz–Morrey spaces.

Sobolev inequalities for riesz potentials of functions in \

Our aim in this paper is to deal with Sobolev inequalities for Riesz potentials of functions in Lebesgue spaces of variable exponents near Sobolev’s exponent over nondoubling metric measure spaces.

l^{p(\cdot )}\

In this paper we are concerned with Trudinger’s inequality and continuity for Riesz potentials of functions in grand Musielak-Orlicz-Morrey spaces over non-doubling metric measure spaces.

over nondoubling measure spaces

Our aim in this note is to estimate the weighted Orlicz-Riesz capacity of balls.

Trudinger’s inequality and continuity for Riesz potentials of functions in grand Musielak–Orlicz–Morrey spaces over nondoubling metric measure spaces

We introduce Herz-Morrey-Orlicz spaces on the half space, and study the boundedness of the Hardy-Littlewood maximal operator. As an application, we establish Sobolev’s inequality for Riesz potentials of functions in such spaces, which is one of mixed norm type inequalities. Mathematics subject classification (2010): 31B15, 46E35.

WEIGHTED ORLICZ-RIESZ CAPACITY OF BALLS

We are concerned with the boundedness of generalized fractional integral operators Iϱ,τ from Orlicz spaces LΦ(X) near L1(X) to Orlicz spaces LΨ(X) over metric measure spaces equipped with lower Ahlfors Q-regular measures, where Φ is a function of the form Φ(r) = rl(r) and l is of log-type. We give a generalization of paper by Mizuta et al. (2010), in the Euclidean setting. We deal with both generalized Riesz potentials and generalized logarithmic potentials.

Sobolev's inequalities for Herz-Morrey-Orlicz spaces on the half space

ABSTRACT Our aim in this paper is to discuss the weak estimate for the maximal and Riesz potential operators in the non-homogeneous central Morrey type space . Further we obtain the strong estimate for Sobolev functions.