Brownian motion hardy spaces and bounded mean oscillation petersen k e
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Using geometric variants of wavelet shrinkage methods, our algorithm preserves corners while enforcing that the smoothed arcs lie in an L2 Sobolev space Hα of order α chosen by the operator. Peller, Vectorial Hankel operators, commutators and related operators of the Schatten von Neumann classes, Integral Equations and Operator Theory 5 1982 , 244-272. Peller, Estimates of functions of Hilbert space operators, similarity to a contraction and related function algebras, Research Problems, Springer Lecture Notes 1043 199 1984 , 199-204. In , the Hardy spaces or Hardy classes H p are certain of on the or. Durrett, Brownian motion and martingales in analysis, Wadsworth Math.

Bourgain, On the similarity problem for polynomially bounded operators on Hilbert space, Israel J. London Mathematical Society Lecture Note Series, No. Paulsen, Tensor products of operator spaces, J. Lebow, A power bounded operator which is not polynomially bounded, Mich. Weighted norm inequalities for Lp and Hp are derived for the Littlewood-Paley function g?. The dyadic counterpart 30 8.

Halmos, Ten problems in Hilbert space, Bull. Bourgain, On the similarity problem for polynomially bounded operators on Hilbert space, Israel J. Here x I is a fixed sequence of bounded scalars. Cuyana 1 1955 , 105-167. Foguel, A counterexample to a problem of Sz. Bourgain, New Banach space properties of the disc algebra and , Acta Math.

Cotlar, A unified theory of Hilbert transforms and ergodic theorems, Rev. In this paper we study families of spaces which are similar in spirit to the Rosenthal class. They were introduced by , who named them after , because of the paper. Lebow, A power bounded operator which is not polynomially bounded, Mich. Sarason, Generalized interpolation in , Trans.

It is shown that some of its properties can be obtained from the general theory of operators of Calderón-Zygmund type which, apparently, has not been considered applicable in this context. } The L 1 and H 1 norms are not equivalent on H 1, and H 1 is not closed in L 1. Peller, Estimates of functions of power bounded operators on Hilbert space, J. Peller, Vectorial Hankel operators, commutators and related operators of the Schatten von Neumann classes, Integral Equations and Operator Theory 5 1982 , 244-272. New results concerning the boundedness of this function are obtained, by a different method of proof, even in the unweighted case.

A polynomially bounded operator on Hilbert space which is not similar to a contraction Author: Journal: J. Coifman and Guido Weiss, Maximal functions and spaces defined by ergodic transformations, Proc. Haagerup, Injectivity and decomposition of completely bounded maps, in Operator Algebras and their Connection with Topology and Ergodic Theory, Springer Lecture Notes in Math. The definition that follows does not distinguish between real or complex case. Durrett, Brownian motion and martingales in analysis, Wadsworth Math.

Pisier, Similarity problems and completely bounded maps, Springer Lecture Notes 1618 1995. Sarason, Generalized interpolation in , Trans. Anosov, On an additive functional homology equation connected with an ergodic rotation of the circle, Izv. Let τ denote the hitting time of the unit circle. Gebiete 23 1972 , 75—82 French. It is shown that H 1 T and H 1 T, l 2 are not isomorphic, which leads to the distinction of H 1 in one and more variables. Duren, Theory of spaces, Academic Press, New York, 1970.

Stein, -spaces of several variables, Acta Math. Rochberg, A Hankel type operator arising in deformation theory, Proc. Treil, Geometric methods in spectral theory of vector valued functions: some recent results, Operator Theory: Adv. . There are also higher-dimensional generalizations, consisting of certain holomorphic functions on in the complex case, or certain spaces of distributions on R n in the real case. Let P r denote the Poisson kernel on the unit circle T. Foguel, A counterexample to a problem of Sz.

Stafney, A class of operators and similarity to contractions, Michigan Math. Paulsen, Tensor products of operator spaces, J. We characterize functions in Q ff R n by means of the Poisson extension, p- Carleson measures, mean oscillation and wavelet coefficients, and give a dyadic counterpart. Halmos, On Foguel's answer to Nagy's question, Proc. We also give some related finite-dimensional estimates. Burkholder, Distribution function inequalities for martingales, Ann. Krieger, On unique ergodicity, Proc.

A simple proof is given of the familiar theorem that any measurable function can be altered on a set of arbitrarily small measure so as to become a function whose Fourier and Fourier-Walsh series converge. Peller, Estimates of functions of Hilbert space operators, similarity to a contraction and related function algebras, Research Problems, Springer Lecture Notes 1043 199 1984 , 199-204. Halmos, On Foguel's answer to Nagy's question, Proc. } This space, sometimes denoted by H 1 δ , is isomorphic to the classical real H 1 space on the circle. Williams, On a class of polynomially bounded operators, Preprint unpublished, 1979 or 1980? Paulsen, Every completely polynomially bounded operator is similar to a contraction, J.