OPTIMAL REARRANGEMENT-INVARIANT BANACH FUNCTION RANGE FOR THE HILBERT TRANSFORM

被引：2

作者：

Tulenov, K. S. ^{[1
,2
]}

机构：

[1] Al Farabi Kazakh Natl Univ, Dept Mech & Math, 71 Al Farabi Ave, Alma Ata 050040, Kazakhstan

[2] Inst Math & Math Modeling, 71 Al Farabi Ave, Alma Ata 050040, Kazakhstan

来源：

EURASIAN MATHEMATICAL JOURNAL | 2021年 / 12卷 / 02期

关键词：

rearrangement-invariant Banach function space; Hilbert transform; optimal range; SOBOLEV IMBEDDINGS; OPTIMAL DOMAIN;

D O I：

10.32523/2077-9879-2021-12-2-90-103

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We describe the optimal rearrangement-invariant Banach function range of the classical Hilbert transform acting on a rearrangement-invariant Banach function space. We also show the existence of such optimal range for the Lorentz and Marcinkiewicz spaces.

引用

页码：90 / 103

页数：14

共 50 条

[21] Boundedness and convergence of martingales in rearrangement-invariant function spaces
M. Kikuchi
Archiv der Mathematik, 2000, 75 : 312 - 320
[22] On the full range of Zippin and inclusion indices of rearrangement-invariant spaces
Curbera, Guillermo P.
Karlovych, Oleksiy
Shargorodsky, Eugene
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2024, 118 (03)
[23] Fractional integral operators on Morrey spaces built on rearrangement-invariant quasi-Banach function spaces
Kwok-Pun Ho
Positivity, 2023, 27
[24] REARRANGEMENT-INVARIANT HULLS OF SETS
GULISASHVILI, AB
LECTURE NOTES IN MATHEMATICS, 1984, 1043 : 642 - 645
[25] MARTINGALE INEQUALITIES IN REARRANGEMENT-INVARIANT FUNCTION-SPACES
JOHNSON, WB
SCHECHTMAN, G
ISRAEL JOURNAL OF MATHEMATICS, 1988, 64 (03) : 267 - 275
[26] BANACH-SAKS TYPE PROPERTIES IN REARRANGEMENT-INVARIANT SPACES WITH THE KRUGLOV PROPERTY
Astashkin, S. V.
Semenov, E. M.
Sukochev, F. A.
HOUSTON JOURNAL OF MATHEMATICS, 2009, 35 (03): : 959 - 973
[27] Optimal behavior of weighted Hardy operators on rearrangement-invariant spaces
Mihula, Zdenek
MATHEMATISCHE NACHRICHTEN, 2023, 296 (08) : 3492 - 3538
[28] Subspaces of rearrangement-invariant spaces
Hernandez, FL
Kalton, NJ
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1996, 48 (04): : 794 - 833
[29] ISOMETRIES ON REARRANGEMENT-INVARIANT SPACES
KALTON, NJ
RANDRIANANTOANINA, B
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1993, 316 (04): : 351 - 355
[30] MARTINGALE INEQUALITIES IN REARRANGEMENT-INVARIANT FUNCTION-SPACES - REMARK
HITCZENKO, P
LECTURE NOTES IN MATHEMATICS, 1991, 1470 : 177 - 182

← 1 2 3 4 5 →