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On Lorentz-Zygmund spaces

Seria
Rozprawy Matematyczne tom/nr w serii: 175 wydano: 1980
Zawartość
Warianty tytułu
Abstrakty
EN

CONTENTS

I. Introduction

 1. The Marcinkiewicz interpolation theorem..................................... 5
 2. The classical results: Theorem B.......................................................... 11
 3. The classical results: Theorem C......................................................... 13
 4. Remarks..................................................................................................... 21

II. Preliminaries

 5. Lorentz spaces; operators of strong and weak types (p, g)...... 22
 6. Variations on Hardy's inequalities......................................................... 24
 7. Averaging operators $A_p$, $B_p$, $G_p$ and $D_p$................... 28

III. The Lorentz-Zygmund spaces

 8. Lorentz-Zygmund spaces Lila{logL)a.......................................... 29
 9. Inclusion relations.................................................................................... 30
 10. The classical function spaces............................................................. 34
 11. The auxiliary spaces $ℒ^{pa}(logℒ)^a$ and $M^{pa}(logM)^a$... 38
 12. The embedding theorem....................................................................... 42

IV. Operators of weak type (p, q; r, s)

 13. Definition and elementary properties.......................................... 43
 14. The Fourier transform............................................................................. 49
 15. The Hardy-Littlewood maximal operator............................................. 49
 16. The (maximal) Hilbert transform........................................................... 50
 17. The fractional integrals........................................................................... 58

V. Proof of the main results

 18. Proof of Theorems B and C........................................................... 59
 19. Connections with interpolation space theory..................................... 62

References........................................................................................................... 65
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 175
Liczba stron
67
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CLXXV
Daty
wydano
1980
Twórcy
  • Department of Mathematics University of South Carolina Columbia, South Carolina 29 208
autor
  • Department of Mathematics Texas A & M University College Station, Texas 77843
Bibliografia
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Identyfikator YADDA
bwmeta1.element.zamlynska-401a9cd7-4787-4b21-8aa9-89494eb535c7
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ISBN
83-01-01111-4
ISSN
0012-3862
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DML-PL
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