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On general Franklin systems

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Gevorkyan G., Kamont A.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS 1. Introduction.....................................................................................5 1.1. Notation......................................................................................7 2. Definition and properties of general Franklin systems..................10 2.1. Piecewise linear functions.........................................................10 2.2. Franklin functions.....................................................................11 2.3. Sequences of partitions and Franklin functions........................13 2.3.1. Regularity of sequences of partitions...................................14 2.4. Sequences of partitions and general Haar systems.................16 2.5. Technical lemmas.....................................................................17 3. Franklin series in $L^p$, 1 < p < ∞...............................................21 4. Franklin series in $L^p$, 0 < p ≤ 1, and $H^p$, 1/2 < p ≤ 1..........27 5. The necessity of strong regularity in $H^p$, 1/2 < p ≤ 1...............42 6. Haar and Franklin series with identical coefficients......................46 7. Characterization of the spaces BMO and Lip(α), 0 < α < 1...........51 References.......................................................................................58

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1 Gevorkyan G.

1 Kamont A.

1 1998

Wyniki wyszukiwania

On general Franklin systems