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On Lorentz-Zygmund spaces

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Bennett C., Rudnick K.

Instytut Matematyczny Polskiej Akademii Nauk

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

Ograniczanie wyników

1 Bennett C.

1 Rudnick K.

1 1980

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On Lorentz-Zygmund spaces