The Fundamental Function of Certain Interpolation Spaces Generated by N-Tuples of Rearrangement-Invariant Spaces

2017 ◽  
pp. 1-14
Author(s):  
Fernando Cobos ◽  
Luz M. Fernández-Cabrera
Keyword(s):  
Interpolation Spaces ◽  
Fundamental Function ◽  
Rearrangement Invariant Spaces ◽  
Invariant Spaces

scholarly journals The K-functional of certain pairs of rearrangement invariant spaces

1983 ◽  
Vol 27 (2) ◽  
pp. 249-257 ◽  
Author(s):  
Jonathan Arazy
Keyword(s):  
Fundamental Function ◽  
Rearrangement Invariant Spaces ◽  
Image Position ◽  
Invariant Spaces

Let X, Y be rearrangement invariant spaces and let M = M(Y, X) be the space of all multipliers of Y into X. It is shown that if X = YM and some technical conditions are satisfied, then the K-functional K(t, f, X, Y) is equivalent to the expressionwhere ψ is the inverse of the fundamental function ϕM of M, defined by

On orthogonality in nonseparable rearrangement invariant spaces

2021 ◽  
Vol 212 (11) ◽  
Author(s):  
Sergei Vladimirovich Astashkin ◽  
Evgenii Mikhailovich Semenov
Keyword(s):  
Rearrangement Invariant Spaces ◽  
Invariant Spaces

Orthogonal Elements in Nonseparable Rearrangement Invariant Spaces

2020 ◽  
Vol 102 (3) ◽  
pp. 449-450
Author(s):  
S. V. Astashkin ◽  
E. M. Semenov
Keyword(s):  
Rearrangement Invariant Spaces ◽  
Invariant Spaces

Hermite Conjugate Functions and Rearrangement Invariant Spaces

1973 ◽  
Vol 16 (3) ◽  
pp. 377-380 ◽  
Author(s):  
Kenneth F. Andersen
Keyword(s):  
Weak Type ◽  
Conjugate Function ◽  
Poisson Integral ◽  
Conjugate Functions ◽  
Rearrangement Invariant Spaces ◽  
Image Position ◽  
Invariant Spaces

The Hermite conjugate Poisson integral of a given f ∊ L1(μ), dμ(y)= exp(—y2) dy, was defined by Muckenhoupt [5, p. 247] aswhereIf the Hermite conjugate function operator T is defined by (Tf) a.e., then one of the main results of [5] is that T is of weak-type (1, 1) and strongtype (p,p) for all p>l.

scholarly journals Boundedness of classical operators on rearrangement-invariant spaces

2020 ◽  
Vol 278 (4) ◽  
pp. 108341 ◽  
Author(s):  
David E. Edmunds ◽  
Zdeněk Mihula ◽  
Vít Musil ◽  
Luboš Pick
Keyword(s):  
Rearrangement Invariant Spaces ◽  
Invariant Spaces
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