Titlebook: Haar Series and Linear Operators; Igor Novikov,Evgenij Semenov Book 1997 Springer Science+Business Media Dordrecht 1997 DEX.Equivalence.Ma

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Fourier-Haar Coefficients,In this section the operator.will be investigated. As usual, . = 2. + ., ., .∈ Ω. Denote

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Haar System Rearrangements,Let . ≥ 0 and π. be a rearrangement of {0,1} if . = 0 and {1, 2, ..., 2.} if . ≥ 1. A sequence π = {π., π. ...} generates the operator

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Pointwise Estimates of Multipliers,Let . be a linear operator acting in a pair of r.i. spaces. An operator .. is said to be a transposed one with respect to .. if for every measurable subsets ., . ? [0,1]. A.P. Calderon proved the following theorem [52]. If . and its transposed operator .. have the weak types (1,1) and (2,2) with norms ≤ 1, then, for every . ∈ (0,1] . where

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Estimates of Multipliers in ,,,Here we use the notations of Chapter 12, 13. If |λ.| ≤ 1 for (.) ∈ Ω, then the corresponding multiplier Λ is of week type (1,1) and its norm is less than 2. This statement was proved in Chapter 5. This chapter is devoted to the unimprovability of the mentioned result.

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Subsequences of the Haar system,If the H.s. is an unconditional basis of an r.i. space ., then the spaces spanned by subsequences of the H.s. are complemented in .. These spaces can be characterized in the following form.

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