In this paper we show the weak Banach-Saks property of the Banach vector space (L p µ) m generated by m L p µ-spaces for 1 ≤ p < +∞, where m is any given natural number. When m = 1, this is the famous Banach-Saks-Szlenk theorem. By use of this property, we also present inequalities for integrals of functions that are the composition of nonnegative continuous convex functions on a convex set of ...

Abstract Let Ω be a compact Hausdorff space, let E be a Banach space, and let C(Ω, E) stand for the Banach space of all E-valued continuous functions on Ω under supnorm. In this paper we study when nuclear operators on C(Ω, E) spaces can be completely characterized in terms of properties of their representing vector measures. We also show that if F is a Banach space and if T : C(Ω, E) → F is a ...

We give direct and inverse approximation theorems for Dirichlet series in Smirnov spaces over convex polygons. We estimate the degree of convergence and the regularity of the functions with moduli of arbitrary order k. Moreover, we consider the influence of differentiability conditions on the rate of approximation and vice versa. This work extends results by Yu. I. Mel’nik and gives an example ...

Let F be a τ -sheaf. Building on previous work of Drinfeld, Anderson, Taguchi, and Wan, Böckle and Pink [BP1] develop a cohomology theory for F . In [Boc1] Böckle uses this theory to establish the analytic continuation of the L-series associated to F (which is a characteristic p valued “Dirichlet series”) and the logarithmic growth of the degrees of its special polynomials. In this paper we sha...

We propose to associate a modular form (an infinite number of) complex valued functions on the $p$-adic numbers $\mathbb{Q}_p$ for each prime $p$. elaborate correspondence and study its consequence in terms of Mellin transforms $L$-functions related forms. Further we discuss case products Dirichlet their duals, which are convolution $\vartheta$-series. The latter intriguingly similar non-holomo...

Some new fixed point theorems for multi-valued operator satisfying increasing properties are proved in partial ordered metric space and in partial ordered Banach space, respectively.

This paper is devoted to the study of reproducing kernel Hilbert spaces. We focus on multipliers of reproducing kernel Banach and Hilbert spaces. In particular, we try to extend this concept and prove some related theorems. Moreover, we focus on reproducing kernels in vector-valued reproducing kernel Hilbert spaces. In particular, we extend reproducing kernels to relative reproducing kernels an...

Let X be a complex Banach space and let Bloch(X) denote the space of X-valued analytic functions on the unit disc verifying that sup|z|<1(1−|z|)||f ′(z)|| < ∞. A sequence (Tn)n of bounded operators between two Banach spaces X and Y is said to be an operator-valued multiplier between Bloch(X) and 1(Y ) if the map ∑∞ n=0 xnz n → (Tn(xn))n defines a bounded linear operator from Bloch(X) into 1(Y )...

We study a Cauchy problem for non-convex valued evolution inclusions in non separable Banach spaces under Filippov type assumptions. We establish existence and relaxation theorems.