Mixed norm space of pluriharmonic functions
MÖbius Transformations and Multiplicative Representations for Spherical Potentials
Modulus and continuous capacity.
Monotonicity of Harnack inequality for positive invariant harmonic functions.
More on existence and uniqueness of decomposition of excessive functions and measures into extremes
More on modified quaternionic analysis in R3.
Multifractals and projections.
In this paper, we generalize the result of Hunt and Kaloshin [5] about the Lq-spectral dimensions of a measure and that of its projections. The results we obtain, allow to study an untreated case in their work and to find a relationship between the multifractal spectrum of a measure and that of its projections.
Multiple layer potentials for the quadrant and their application to the Dirichlet problem in plane domains with a piecewise smooth boundary
Multiplication of subharmonic functions.
Multiplicative square functions.
We study regularity properties of a positive measure in the euclidean space in terms of two square functions which are the multiplicative analogues of the usual martingale square function and of the Lusin area function of a harmonic function. The size of ...
Multipliers of the Vanishing Hardy Classes
Multiply superharmonic functions
Some results concerning the multiply superharmonic functions and the boundary behaviour are given and some problems involving these notions are described.
Multivariate smooth interpolation that employs polyharmonic functions
We study the problem of construction of the smooth interpolation formula presented as the minimizer of suitable functionals subject to interpolation constraints. We present a procedure for determining the interpolation formula that in a natural way leads to a linear combination of polyharmonic splines complemented with lower order polynomial terms. In general, such formulae can be very useful e.g. in geographic information systems or computer aided geometric design. A simple computational example...
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....