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Adaptive Deterministic Dyadic Grids on Spaces of Homogeneous Type

Lechner R., Passenbrunner M.

Bulletin of the Polish Academy of Sciences. Mathematics

2014

Vol. 62, no 2

139--159

In the context of spaces of homogeneous type, we develop a method to deterministically construct dyadic grids, specifically adapted to a given combinatorial situation. This method is used to estimate vector-valued operators rearranging martingale difference sequences such as the Haar system.

Some generalized spaces of vector valued double sequences defined by a modulus

Subramanian N.

Fasciculi Mathematici

2013

Nr 51

159--172

In this paper we generalize the xf2 by introducing the sequence space xfmn2 (Δ(ηϒ)μ,p,q,r) and exhibit some general properties of the space.

The One-Third-Trick and Shift Operators

Lechner R.

Bulletin of the Polish Academy of Sciences. Mathematics

2013

Vol. 61, no 3-4

219--238

We obtain a representation as martingale transform operators for the rearrangement and shift operators introduced by T. Figiel. The martingale transforms and the underlying sigma algebras are obtained explicitly by combinatorial means. The known norm estimates for those operators are a direct consequence of our representation.

Spaces of entire functions represented by vector valued Dirichlet series

Srivastava G. S., Sharma A.

Journal of Mathematics and Applications

2011

Vol. 34

97--107

Spaces of entire functions ƒ represented by vector valued Dirichlet series and having finite order and finite type are considered. These are endowed with a certain topology under which they become a Frechet space. On this space the form of linear continuous functionals is characterized. Proper bases are also characterized in terms of growth parameters.