we establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. as an application, we obtain the $(l^p, l^q)$-norm inequality for vector-valued multilinear operators.

Let X = P εnxn be a Rademacher series with vector-valued coefficients. We obtain an approximate formula for the distribution of the random variable ||X|| in terms of its mean and a certain quantity derived from the K-functional of interpolation theory. Several applications of the formula are given.

The space of entire functions represented by Dirichlet series of several complex variables has been studied by S. Dauod [1]. M.D. Patwardhan [6] studied the bornological properties of the space of entire functions represented by power series. In this work we study the bornological aspect of the space Γ of entire functions represented by Dirichlet series of several complex variables. By Γ we den...

We study uniqueness of the recovery a time-dependent magnetic vector-valued potential and an electric scalar-valued on Riemannian manifold from knowledge Dirichlet to Neumann map hyperbolic equation. The Cauchy data is observed time-like parts space-time boundary proved up natural gauge for problem. proof based Gaussian beams inversion light ray transform Lorentzian manifolds under assumptions ...

The trace formula for SL{2,Z) can be developed for vector-valued functions which satisfy an automorphic condition involving a group representation n . This paper makes this version explicit for the class of representations which can be realized as representations of the finite group PSL(2,Z/q) for some prime q . The body of the paper is devoted to computing, for the singular representations n ,...

In this paper, we consider a random entire function f(s, ω) defined by a random Dirichlet series ∑∞ n=1Xn(ω)e −λns whereXn are independent and complex valued variables, 0 6 λn ր +∞. We prove that under natural conditions, for some random entire functions of order (R) zero f(s, ω) almost surely every horizontal line is a Julia line without an exceptional value. The result improve a theorem of J....

We give some remarks on two-dimensional multiple-valued Dirichlet minimizing functions, including frequency, classification of branch points and their connections. As an application, we prove that blowing-up functions of a two-dimensional multiple-valued Dirichlet minimizing function are unique. This paper is concluded with a boundary regularity theorem for two-dimensional multiple-valued Diric...

The main aim of this paper is to obtain a converse theorem for double Dirichlet series and use it to show that the Shintani zeta functions [13] which arise in the theory of prehomogeneous vector spaces are actually linear combinations of Mellin transforms of metaplectic Eisenstein series on GL(2). The converse theorem we prove will apply to a very general family of double Dirichlet series which...