scholarly journals Some Reiteration Theorems for R , L , R R , R L , L R , and L L Limiting Interpolation Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-31
Author(s):  
Leo R. Ya. Doktorski
Keyword(s):  
Lorentz Spaces ◽  
Interpolation Spaces ◽  
Interpolation Methods

We consider the K -interpolation methods involving slowly varying functions. We establish some reiteration formulae including so-called L or R limiting interpolation spaces as well as the R R , R L , L R , and L L extremal interpolation spaces. These spaces arise in the limiting situations. The proofs of most reiteration formulae are based on Holmstedt-type formulae. Applications to grand and small Lorentz spaces in critical cases are given.

scholarly journals Interpolation of Gentle Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Mourad Ben Slimane ◽  
Hnia Ben Braiek
Keyword(s):  
Function Space ◽  
Nonlinear Approximation ◽  
Lorentz Spaces ◽  
Complex Interpolation ◽  
Interpolation Spaces ◽  
Wavelet Coefficients ◽  
The Stability

The notion of gentle spaces, introduced by Jaffard, describes what would be an “ideal” function space to work with wavelet coefficients. It is based mainly on the separability, the existence of bases, the homogeneity, and theγ-stability. We prove that real and complex interpolation spaces between two gentle spaces are also gentle. This shows the relevance and the stability of this notion. We deduce that Lorentz spacesLp,qandHp,qspaces are gentle. Further, an application to nonlinear approximation is presented.

scholarly journals Reiteration Formulae for the Real Interpolation Method Including L or R Limiting Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Leo R. Ya. Doktorski
Keyword(s):  
Interpolation Method ◽  
Lorentz Spaces ◽  
Real Interpolation ◽  
Interpolation Spaces ◽  
The Real ◽  
Real Interpolation Method

We consider a real interpolation method defined by means of slowly varying functions. We present some reiteration formulae including so-called L or R limiting interpolation spaces. These spaces arise naturally in reiteration formulae for the limiting cases θ = 0 or θ = 1 . Applications to grand and small Lorentz spaces are given.

scholarly journals K-ENVELOPES FOR REAL INTERPOLATION METHODS

2012 ◽  
Vol 55 (2) ◽  
pp. 293-307
Author(s):  
MING FAN
Keyword(s):  
Function Space ◽  
Upper Bounds ◽  
Function Spaces ◽  
Real Interpolation ◽  
Rearrangement Invariant Space ◽  
Interpolation Spaces ◽  
Invariant Space ◽  
Bounded Operators ◽  
Fundamental Function ◽  
Interpolation Methods

AbstractIn this paper, we study the K-envelopes of the real interpolation methods with function space parameters in the sense of Brudnyi and Kruglyak [Y. A. Brudnyi and N. Ja. Kruglyak, Interpolation functors and interpolation spaces (North-Holland, Amsterdam, Netherlands, 1991)]. We estimate the upper bounds of the K-envelopes and the interpolation norms of bounded operators for the KΦ-methods in terms of the fundamental function of the rearrangement invariant space related to the function space parameter Φ. The results concerning the quasi-power parameters and the growth/continuity envelopes in function spaces are obtained.

Interpolation spaces and interpolation methods

1965 ◽  
Vol 68 (1) ◽  
pp. 51-117 ◽  
Author(s):  
N. Aronszajn ◽  
E. Gagliardo
Keyword(s):  
Interpolation Spaces ◽  
Interpolation Methods

Effects of Sampling and Interpolation Methods on Accuracy of Extracted Watershed Features

2021 ◽  
Vol 26 (3) ◽  
pp. 05020053
Author(s):  
Jingwei Hou ◽  
Meiyan Zheng ◽  
Moyan Zhu ◽  
Yanjuan Wang
Keyword(s):  
Interpolation Methods

scholarly journals Spatio-Temporal Analysis of Water Quality Parameters in Machángara River with Nonuniform Interpolation Methods

Water ◽  
2016 ◽  
Vol 8 (11) ◽  
pp. 507 ◽  
Author(s):  
Iván Vizcaíno ◽  
Enrique Carrera ◽  
Margarita Sanromán-Junquera ◽  
Sergio Muñoz-Romero ◽  
José Luis Rojo-Álvarez ◽  
...  
Keyword(s):  
Water Quality ◽  
Temporal Analysis ◽  
Quality Parameters ◽  
Water Quality Parameters ◽  
Interpolation Methods ◽  
Spatio Temporal

A genuine analogue of the Wiener Tauberian theorem for some Lorentz spaces on SL(2,ℝ)

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Tapendu Rana
Keyword(s):  
Tauberian Theorem ◽  
Lorentz Spaces

AbstractIn this paper, we prove a genuine analogue of the Wiener Tauberian theorem for {L^{p,1}(G)} ({1\leq p<2}), with {G=\mathrm{SL}(2,\mathbb{R})}.

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