An estimate of the Wiman-Valiron type for a maximum modulus on a polydisk of an entire function of several complex variables is obtained. The estimate contains a weight function involved also in the calculation of the radius of the admissible ball.

A Brezis–Gallouet–Wainger logarithmic interpolation-embedding inequality is proved for various classes of irregular domains, in particular, for power cusps and λ-John domains.

This is a survey of results mostly relating elliptic equations and systems of arbitrary even order with rough coefficients in Lipschitz graph domains. Asymptotic properties of solutions at a point of a Lipschitz boundary are also discussed.

We study the Dirichlet problem, in Lipschitz domains and with boundary data in Besov spaces, for divergence form strongly elliptic systems of arbitrary order with bounded, complex-valued coefficients. A sharp corollary of our main solvability result is that the operator of this problem performs an isomorphism between weighted Sobolev spaces when its coefficients and the unit normal of the boundary belong to the space VMO.

Necessary and sufficient conditions for a function to be a multiplier mapping the Besov space B-1(m)(R-n) into the Besov space B-1(l)(R-n) with integer l and m, 0 < l <= m, are found. It is shown that multipliers between B-1(m)(R-n) and B-1(l)(R-n) form the space of traces of multipliers between the Sobolev classes W-1(m+1)(R-+(n+1)) and W-1(l+1)(R-+(n+1)).

The goal of this work is to study the inhomogeneous Dirichlet problem for the Stokes system in a Lipschitz domain Omega aS dagger a"e (n) , na (c) 3/42. Our main result is that this problem is well posed in Besov-Triebel-Lizorkin spaces, provided that the unit normal nu to Omega has small mean oscillation.