Boundary limits of spherical means for BLD and monotone BLD functions in the unit ball.
Growth properties of spherical means for monotone BLD functions in the unit ball.
Sobolev embeddings for variable exponent Riesz potentials on metric spaces.
Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces
Our aim in this paper is to deal with the boundedness of the Hardy-Littlewood maximal operator on grand Morrey spaces of variable exponents over non-doubling measure spaces. As an application of the boundedness of the maximal operator, we establish Sobolev's inequality for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces. We are also concerned with Trudinger's inequality and the continuity for Riesz potentials.
Musielak-Orlicz-Sobolev spaces on metric measure spaces
Our aim in this paper is to study Musielak-Orlicz-Sobolev spaces on metric measure spaces. We consider a Hajłasz-type condition and a Newtonian condition. We prove that Lipschitz continuous functions are dense, as well as other basic properties. We study the relationship between these spaces, and discuss the Lebesgue point theorem in these spaces. We also deal with the boundedness of the Hardy-Littlewood maximal operator on Musielak-Orlicz spaces. As an application of the boundedness of the Hardy-Littlewood...
Musielak-Orlicz-Sobolev spaces with zero boundary values on metric measure spaces
We define and study Musielak-Orlicz-Sobolev spaces with zero boundary values on any metric space endowed with a Borel regular measure. We extend many classical results, including completeness, lattice properties and removable sets, to Musielak-Orlicz-Sobolev spaces on metric measure spaces. We give sufficient conditions which guarantee that a Sobolev function can be approximated by Lipschitz continuous functions vanishing outside an open set. These conditions are based on Hardy type inequalities....
Generalized fractional integral operators on weak Choquet spaces over quasi-metric measure spaces
We prove the boundedness of the generalized fractional maximal operator and the generalized fractional integral operator on weak Choquet spaces with respect to Hausdorff content over quasi-metric measure spaces.
Optimal estimates for the fractional Hardy operator
Let be the n-dimensional fractional Hardy operator, where 0 < α ≤ n. It is well-known that is bounded from to with when n(1-1/p) < α ≤ n. We improve this result within the framework of Banach function spaces, for instance, weighted Lebesgue spaces and Lorentz spaces. We in fact find a ’source’ space , which is strictly larger than X, and a ’target’ space , which is strictly smaller than Y, under the assumption that is bounded from X into Y and the Hardy-Littlewood maximal operator...
Boundedness of generalized fractional integral operators on Orlicz spaces near over metric measure spaces
We are concerned with the boundedness of generalized fractional integral operators from Orlicz spaces near to Orlicz spaces over metric measure spaces equipped with lower Ahlfors -regular measures, where is a function of the form and 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.
Approximate identities and Young type inequalities in Musielak-Orlicz spaces
We discuss the convergence of approximate identities in Musielak-Orlicz spaces extending the results given by Cruz-Uribe and Fiorenza (2007) and the authors F.-Y. Maeda, Y. Mizuta and T. Ohno (2010). As in these papers, we treat the case where the approximate identity is of potential type and the case where the approximate identity is defined by a function of compact support. We also give a Young type inequality for convolution with respect to the norm in Musielak-Orlicz spaces.
Trudinger's inequality for double phase functionals with variable exponents
Our aim in this paper is to establish Trudinger’s inequality on Musielak-Orlicz-Morrey spaces under conditions on which are essentially weaker than those considered in a former paper. As an application and example, we show Trudinger’s inequality for double phase functionals , where and satisfy log-Hölder conditions and is nonnegative, bounded and Hölder continuous.
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