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Boundedness of Toeplitz type operators associated to Riesz potential operator with general kernel on Orlicz space

100%

Chen D.

Open Mathematics

2015

tom 13

nr 1

In this paper, the boundedness properties for some Toeplitz type operators associated to the Riesz potential and general integral operators from Lebesgue spaces to Orlicz spaces are proved. The general integral operators include singular integral operator with general kernel, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.

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On general Franklin systems

88%

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

Ograniczanie wyników

1 Open Mathematics

1 Chen D.

1 Gevorkyan G.

1 Kamont A.

1 2015

1 1998

Wyniki wyszukiwania

Boundedness of Toeplitz type operators associated to Riesz potential operator with general kernel on Orlicz space

On general Franklin systems