Tangential limits of monotone Sobolev functions.
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.
Lindelöf theorems for monotone Sobolev functions.
Sobolev embeddings for variable exponent Riesz potentials on metric spaces.
Continuity properties of Riesz potentials and boundary limits of Beppo Levi functions.
On the boundary limits of harmonic functions with gradient in
This paper deals with tangential boundary behaviors of harmonic functions with gradient in Lebesgue classes. Our aim is to extend a recent result of Cruzeiro (C.R.A.S., Paris, 294 (1982), 71–74), concerning tangential boundary limits of harmonic functions with gradient in , denoting the upper half space of the -dimensional euclidean space . Our method used here is different from that of Nagel, Rudin and Shapiro (Ann. of Math., 116 (1982), 331–360); in fact, we use the integral representation...
On the existence of weighted boundary limits of harmonic functions
We study the existence of tangential boundary limits for harmonic functions in a Lipschitz domain, which belong to Orlicz-Sobolev classes. The exceptional sets appearing in this discussion are evaluated by use of Bessel-type capacities as well as Hausdorff measures.
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...
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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