General Reiteration Theorems for R and L Classes: Case of Right R-Spaces and Left L-Spaces

被引：6

作者：

Fernandez-Martinez, Pedro ^{[1
]}

Signes, Teresa M. ^{[1
]}

机构：

[1] Univ Murcia, Dept Matemat, Fac Matemat, Campus Espinardo, Espinardo 30071, Spain

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2022年 / 19卷 / 04期

基金：

英国工程与自然科学研究理事会;

关键词：

Real interpolation; K-functional; reiteration theorems; slowly varying functions; rearrangement invariant spaces; REAL INTERPOLATION; LIMITING INTERPOLATION; PARAMETER; GRAND;

D O I：

10.1007/s00009-022-02059-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given E-0, E-1, E, F rearrangement invariant spaces, a, b, b(0), b(1) slowly varying functions and 0 <= theta(0) < theta(1) <= 1, we characterize the interpolation spaces (<(X)over bar>(theta)(0) (,b0,)(E0),(X) over bar (R)(theta 1)(,)(b1)(,)(E1)(,a,F))(theta,b,E) and ((X) over bar (L)(theta 0,)(b0)(,)(E0)(,a,F), (X) over bar (theta 1,)(b1)(,)(E1))(theta,b,E), for all possible values of theta is an element of [0,1]. Applications to interpolation identities for grand and small Lebesgue spaces, Gamma spaces and A and B-type spaces are given.

引用

页数：36

共 50 条

[41] Isomorphic classification of the spaces $H^k_{\rm loc}(\Bbb R)\cap L^2(\Bbb R)$
A. A. Albanese
J. C. Díaz
G. Metafune
Archiv der Mathematik, 1999, 73 : 33 - 41
[42] The Boundedness of Littlewood-Paley Operators with Rough Kernels on Weighted (L~q , L~p )~α (R~n) Spaces
Ximei Wei
Shuangping Tao
AnalysisinTheoryandApplications, 2013, 29 (02) : 135 - 148
[43] General form of the Arrow-Barankin-Blackwell theorem in normed spaces and the l∞-case
Ferro, F., 1600, (79):
[44] Note on Jackson and Bernstein type approximation theorems in the case of approximation by algebraic polynomials in the spaces L and C
Pawelke, S
STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 2000, 36 (3-4) : 353 - 358
[45] Infinite Dimensional Widths and Optimal Recovery of a Function Class in Orlicz Spaces in L(R) Metric
Li, Xinxin
Wu, Garidi
JOURNAL OF MATHEMATICS, 2023, 2023
[46] Greediness of higher rank Haar wavelet bases in L-w(p)(R) spaces
Kapanadze, Ekaterine
STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2014, 59 (02): : 213 - 219
[47] MINIMAL QUADRATURE-FORMULAS FOR THE SPACES H2R AND L2R - A UNIFIED INTERPOLATORY APPROACH
MERSCHEN, BA
COMPUTING, 1985, 34 (02) : 169 - 177
[48] Estimates of the Lebesgue function of Fourier sums in trigonometric polynomials orthogonal with a weight not belonging to the spaces L r (r > 1)
Badkov, V. M.
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2012, 277 : 21 - 32
[49] Estimates of the Lebesgue function of Fourier sums over trigonometric polynomials orthogonal with a weight not belonging to the spaces L-r (r > 1)
Badkov, V. M.
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2011, 17 (03): : 71 - 82
[50] RIGHT-LEFT (R-L) LIVER LOBE RATIO - A SENSITIVE AND SPECIFIC CRITERION FOR CIRRHOSIS
SHREINER, DP
BARLAIKOVACH, M
JOURNAL OF NUCLEAR MEDICINE, 1980, 21 (06) : P76 - P76

← 1 2 3 4 5 →