12 citations · 29 across the 11 of their papers we have counts for
14 papers · 1 filter
Martingale Type, the Gamlen-Gaudet Construction and a Greedy Algorithm
Krystian Kazaniecki, Paul F. X. Müller
In the present paper we identify those filtered probability spaces that determine already the martingale type of a…
Almost everywhere Convergence of Spline Sequences
Paul F. X. Müller, Markus Passenbrunner
We prove the analogue of the Martingale Convergence Theorem for polynomial spline sequences. Given a natural number and a sequence of knots in with multiplicit…
Conditional Square Functions, the Sine-Cosine Decomposition for Hardy Martingales and Dyadic Perturbation
Paul F. X. Müller
We prove that the norm estimate between a Hardy martingale and its cosine part are stable under dyadic perturbations, and show how dyadic stability of the norm es…
Interpolation for Hardy Spaces: Marcinkiewicz decomposition, Complex Interpolation and Holomorphic Martingales
Paul F. X. Müller, Peter Yuditskii
The real and complex interpolation spaces for the classical Hardy spaces and were determined in 1983 by P.W. Jones. Due to the analytic constraints the associated…
Absolutely summing operators and atomic decomposition in bi-parameter Hardy spaces
Paul F. X. Müller, Johanna Penteker
For , , with Haar expansion we constructively determine the Pietsch measure of the -summing multiplication operat…
Factorization of the identity through operators with large diagonal
Niels Jakob Laustsen, Richard Lechner, Paul F. X. Müller
Given a Banach space~ with an unconditional basis, we consider the following question: does the identity on~ factor through every operator on~ with large diagonal relative…
A Decomposition for Hardy Martingales III
Paul F. X. Müller
We prove Davis decompositions for vector valued Hardy martingales and illustrate their use. This paper continues our previous work on Davis and Garsia inequalities for scalar Hardy…
Localization and projections on bi-parameter BMO
Richard Lechner, Paul F. X. Müller
We prove that for any operator on bi--parameter BMO the identity factors through or . Bourgain's localization method provides the conceptual framework of our proof.…
Combinatorics of Dyadic Intervals: Consistent Colorings
Anna Kamont, Paul F. X. Muller
We study the problem of consistent and homogeneous colourings for increasing families of dyadic intervals. We determine when this problem can be solved and when not.
Interpolatory Estimates, Riesz Transforms and Wavelet Projections
Paul F. X. Müller, Stefan Mueller
We prove that directional wavelet projections and Riesz transforms are related by interpolatory estimates. The exponents of interpolation depend on the Hölder estimates of the wave…
A thin-thick Decomposition for Hardy Martingales
Paul F. X. Mueller
We prove thin-thick decompositions, for the class of Hardy martingales and thereby strengthen its square function characterization. We apply the underlying method to several classi…
A Representation Theorem for Singular Integral Operators on Spaces of Homogeneous Type
Paul F. X. Mueller, Markus Passenbrunner
Let (X,d,μ) be a space of homogeneous type and E a UMD Banach space. Under the assumption mu({x})=0 for all x in X, we prove a representation theorem for singular integral operator…
Extrapolation of Vector valued Rearrangement Operators
Stefan Geiss, Paul F. X. Mueller
We study the extrapolation properties of vector valued rearrangement operators acting on the normalized Haar basis in
Extrapolation of Vector valued Rearrangement Operators II
Paul F. X. Mueller
We determine the extrapolation law for rearrangement operators of the Haar system on vector valued Hardy spaces.