We estimate the essential norm of a weighted composition operator relatively to the class of Dunford-Pettis operators or the class of weakly compact operators, on the space H∞ of Dirichlet series. As particular cases, we obtain the precise value of the generalized essential norm of a composition operator and of a multiplication operator.

We consider the wave equation in an unbounded conical domain, with initial conditions and boundary conditions of Dirichlet or Neumann type. We give a uniform decay estimate of the solution in terms of weighted Sobolev norms of the initial data. The decay rate is the same as in the full space case.

This paper presents a Meyer–Vietoris type gluing formula for conformal invariant of Riemannian surface with boundary that is defined by the determinant Dirichlet-to-Neumann operator. The used to bound asymptotics under degeneration. It shown associated height function on moduli space hyperbolic surfaces geodesic proper only in genus zero. Properness implies compactness theorem Steklov isospectr...

The definition of classical holomorphic function spaces such as the Hardy space or Dirichlet on Hartogs triangle is not canonical. In this paper we introduce a natural family which includes some weighted Bergman spaces, candidate and space. For study L p mapping properties Szeg? projection respectively, whereas for prove it isometric to bidisc.

We present forms of the classical Riesz–Kolmogorov theorem for compactness that are applicable in a wide variety settings. In particular, our theorems apply to classify precompact subsets Lebesgue space $$L^2$$ , Paley–Wiener spaces, weighted Bargmann–Fock and scale Besov–Sobolev spaces holomorphic functions includes Bergman general domains as well Hardy Dirichlet space. criteria characterize c...