In this paper we introduce the family of spaces RM(p,q), 1≤p,q≤+∞. They are holomorphic functions in unit disc with average radial integrability. This contains classical Hardy (when p=∞) and Bergman p=q). We characterize inclusion between RM(p1,q1) RM(p2,q2) depending on parameters. For 1<p,q<∞, our main result provides a characterization dual RM(p,q) by means boundedness projection. show that ...

X iv :m at h/ 04 06 10 8v 1 [ m at h. FA ] 6 J un 2 00 4 QUADRATIC REVERSES OF THE CONTINUOUS TRIANGLE INEQUALITY FOR BOCHNER INTEGRAL OF VECTOR-VALUED FUNCTIONS IN HILBERT SPACES SEVER S. DRAGOMIR Abstract. Some quadratic reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are prov...

The theory of  continuous frames in Hilbert spaces is extended, by using the concepts of measure spaces, in order to get the results of a new application of operator theory.  The $K$-frames were  introduced by G$breve{mbox{a}}$vruta (2012) for Hilbert spaces to study atomic systems with respect to a bounded linear operator. Due to the structure of  $K$-frames, there are many differences between...

The aim of this paper is to construct a generalized Fourier analysis for certain Hermitian operators. When A, B are entire functions, then H(A,B) will be the associated reproducing kernel Hilbert spaces of Cn×n-valued functions. In that case, we will construct the expansion theorem forH(A,B) in a comprehensive manner. The spectral functions for the reproducing kernel Hilbert spaces will also be...

We compute the exact value of essential norm a generalized Hilbert matrix operator acting on weighted Bergman spaces Avp and Banach Hv? analytic functions, where v is general radial weight. In particular, we obtain classical standard A?p for p>2+?,??0, Korenblum H?? 0<?<1. also cover Hardy space Hp,1<p<?, case. case, equal to conjectured its similarly in case coincide. Hw?? with weights w?(z)=(...