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A simplification in the proof of the non-isomorphism between H¹(δ) and H¹(δ²)

100%

Müller P.

Studia Mathematica

2002

tom 150

nr 1

13-16

The proof that H¹(δ) and H¹(δ²) are not isomorphic is simplified. This is done by giving a new and simple proof to a martingale inequality of J. Bourgain.

Combinatorics of Dyadic Intervals: Consistent Colourings

63%

Kamont A. , Müller P.

Bulletin of the Polish Academy of Sciences. Mathematics

2014

tom 62

nr 2

101-115

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 it cannot.

A martingale approach to general Franklin systems

63%

Kamont A. , Müller P.

Studia Mathematica

2006

tom 177

nr 3

251-275

We prove unconditionality of general Franklin systems in $L^{p}(X)$, where X is a UMD space and where the general Franklin system corresponds to a quasi-dyadic, weakly regular sequence of knots.

A remark on extrapolation of rearrangement operators on dyadic $H^{s}$, 0 < s ≤ 1

51%

Geiss S. , Müller P. , Pillwein V.

Studia Mathematica

2005

tom 171

nr 2

196-205

For an injective map τ acting on the dyadic subintervals of the unit interval [0,1) we define the rearrangement operator $T_{s}$, 0 < s < 2, to be the linear extension of the map $(h_{I})/(|I|^{1/s}) ↦ (h_{τ(I)})(|τ(I)|^{1/s})$, where $h_{I}$ denotes the $L^{∞}$-normalized Haar function supported on the dyadic interval I. We prove the following extrapolation result: If there exists at least one 0 < s₀ < 2 such that $T_{s₀}$ is bounded on $H^{s₀}$, then for all 0 < s < 2 the operator $T_{s}$ is bounded on $H^{s}$.