A class is studied of complex valued functions defined on the unit disk (with a possible exception of a discrete set) with the property that all their Pick matrices have not more than a prescribed number of negative eigenvalues. Functions in this class, known to appear as pseudomultipliers of the Hardy space, are characterized in several other ways. It turns out that a typical function in the c...

jachymski [ proc. amer. math. soc., 136 (2008), 1359-1373] gave modified version of a banach fixed point theorem on a metric space endowed with a graph. in the present paper, (g, φ)-graphic contractions have been de ned by using a comparison function and studied the existence of fixed points. also, hardy-rogers g-contraction have been introduced and some fixed point theorems have been proved. s...

Fourier spectrum of the boundary values of functions in the complex Hardy Space H(C+) is characterized for p ∈ (0, 2). First, functions f in the L(R) can be decomposed into a sum g + h, where g and h are the non-tangential boundary limits of function in H(C+) and H(C−) in the sense of L(R), where H(C+) and H(C−) are the Hardy spaces in the upper and lower complex plane C+ and C−, respectively. ...

The principal objects of study in this thesis are the noncommutative Hardy algebras introduced by Muhly and Solel in 2004, also called simply “Hardy algebras,” and their quotients by ultraweakly closed ideals. The Hardy algebras form a class of nonselfadjoint dual operator algebras that generalize the classical Hardy algebra, the noncommutative analytic Toeplitz algebras introduced by Popescu i...

In a previous paper [Constrained Hardy Space Approximation, preprint available at http://www.mathematik.uni-karlsruhe.de/iwrmm/seite/ preprints/] we considered the problem of minimizing the distance ‖f − φ‖Lp(K), where K is a subset of the complex unit circle ∂D and φ ∈ C(K), subject to the constraint that f lies in the Hardy space H(D) and |f | ≤ g for some positive function g. This problem oc...

A relevant difference between (9) and least squares formulations is that the former can be used to prove k-explicit stability bounds on u, while the seconds requires these bounds to be well-posed. We note that, using an appropriate operator T : V → V , any well-posed formulation in the form (2) can be translated in a sign-definite one: aT (u, v) := a(u, T v) = F (Tv) =: FT (v). However, the ope...

We continue the study of multilinear operators given by products of finite vectors of Calderón-Zygmund operators. We determine the set of all r ≤ 1 for which these operators map products of Lebesgue spaces Lp(Rn) into the Hardy spaces Hr(Rn). At the endpoint case r = n/n+m+ 1, where m is the highest vanishing moment of the multilinear operator, we prove a weak type result. 0. Introduction A wel...

We adopt the following convention: x1, x2, z are sets, A is a non empty set, and f , g, h are elements of CA. Let us consider A. The functor +CA yielding a binary operation on CA is defined by: (Def. 1) For all elements f , g of CA holds +CA(f, g) = (+C)◦(f, g). Let us consider A. The functor ·CA yielding a binary operation on CA is defined as follows: (Def. 2) For all elements f , g of CA hold...