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1
Content available remote

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
EN
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.
2
Content available remote

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
EN
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.
3
Content available remote

A martingale approach to general Franklin systems

63%
Kamont A., Müller P.
Studia Mathematica
|
2006
|
tom 177
|
nr 3
251-275
EN
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.
4
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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
EN
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 $H^{s}$.
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