Traces of pluriharmonic functions on the boundaries of analytic varieties.
We discuss problems on Hankel determinants and the classical moment problem related to and inspired by certain Vandermonde determinants for polynomial interpolation on (quadratic) algebraic curves in ℂ².
First, noncompact Cantor sets along with their defining trees are introduced as a natural generalization of -adic numbers. Secondly we construct a class of jump processes on a noncompact Cantor set from given pairs of eigenvalues and measures. At the same time, we have concrete expressions of the associated jump kernels and transition densities. Then we construct intrinsic metrics on noncompact Cantor set to obtain estimates of transition densities and jump kernels under some regularity conditions...
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.
Necessary and sufficient conditions governing two-weight norm estimates for multiple Hardy and potential operators are presented. Two-weight inequalities for potentials defined on nonhomogeneous spaces are also discussed. Sketches of the proofs for most of the results are given.