Weak solutions to the complex Hessian equation
We investigate the class of functions associated with the complex Hessian equation .
Weighted norm inequalities for Riesz potentials and fractional maximal functions in mixed norm Lebesgue spaces
Weighted norm inequalities for the Lusin area integral and the nontangential maximal functions for functions harmonic in a Lipschitz domain
Weighted Poincaré-type estimates for conjugate -harmonic tensors.
Weighted polynomial approximation in the complex plane.
Weighted Sobolev spaces and capacity.
Weighted two-parameter Bergman space inequalities.
When finely continuous functions are of the first class of Baire
Whitney's extension theorem for nonquasianalytic classes of ultradifferentiable functions
Wiener's Criterion in Potential Theory with Applications to Nilpotent Lie Groups.
Wiener's test of thinness in potential theory
Wiener's type regularity criteria on the complex plane
We present a number of Wiener’s type necessary and sufficient conditions (in terms of divergence of integrals or series involving a condenser capacity) for a compact set E ⊂ ℂ to be regular with respect to the Dirichlet problem. The same capacity is used to give a simple proof of the following known theorem [2, 6]: If E is a compact subset of ℂ such that for 0 < t ≤ 1 and a ∈ E, where d(F) is the logarithmic capacity of F, then the Green function of ℂ E with pole at infinity is Hölder continuous....
Zero distributions via orthogonality
We develop a new method to prove asymptotic zero distribution for different kinds of orthogonal polynomials. The method directly uses the orthogonality relations. We illustrate the procedure in four cases: classical orthogonality, non-Hermitian orthogonality, orthogonality in rational approximation of Markov functions and its non- Hermitian variant.
Zero sets of functions in harmonic Hardy spaces.
Zero Sets of Non-Negative Strictly Plurisubharmonic Functions.
Zeros of Sequences of Partial Sums and Overconvergence
2000 Mathematics Subject Classification: 30B40, 30B10, 30C15, 31A15.We are concerned with overconvergent power series. The main idea is to relate the distribution of the zeros of subsequences of partial sums and the phenomenon of overconvergence. Sufficient conditions for a power series to be overconvergent in terms of the distribution of the zeros of a subsequence are provided, and results of Jentzsch-Szegö type about the asymptotic distribution of the zeros of overconvergent subsequences are stated....
Zur Holomorphie des Poissonintegrals.
Zur Integration der Differentialgleichung ... = 0.
Zur numerischen Lösung des ersten biharmonischen Randwertproblems.
α-stable random walk has massive thorns
We introduce and study a class of random walks defined on the integer lattice -a discrete space and time counterpart of the symmetric α-stable process in . When 0 < α <2 any coordinate axis in , d ≥ 3, is a non-massive set whereas any cone is massive. We provide a necessary and sufficient condition for a thorn to be a massive set.