Type and cotype are computed for Banach spaces generated by some positive sublinear operators and Banach function spaces. Applications of the results yield that under certain assumptions Clarkson’s inequalities hold in these spaces.

Every isometric property of Banach spaces preserved by real or complex interpolation is subspace-hereditary, and every isomorphic property of separable Banach spaces so preserved is quotient-hereditary. Introduction Many properties of Banach spaces are known to pass to interpolation spaces obtained from the real k-method of interpolation or from the complex method, completeness itself being the...

in this paper we will prove that if $l$ is a continuous symmetric n-linear form on a hilbert spaceand $widehat{l}$ is the associated continuous n-homogeneous polynomial, then $||l||=||widehat{l}||$.for the proof we are using a classical generalized  inequality due to s. bernstein for entire functions of exponential type. furthermore we study the case that if x is a banach space then we have tha...

Interest in Sobolev type equations has recently increased signi cantly, moreover, there arose a necessity for their consideration in quasi-Banach spaces. The need is dictated not so much by the desire to ll up the theory but by the aspiration to comprehend nonclassical models of mathematical physics in quasi-Banach spaces. Notice that the Sobolev type equations are called evolutionary if soluti...