Complex interpolation of Besov-type spaces on domains

2021 ◽  
Author(s):  
Ciqiang Zhuo
Keyword(s):  
Complex Interpolation ◽  
Type Spaces ◽  
Besov Type Spaces

COMPLEX INTERPOLATION ON BESOV-TYPE AND TRIEBEL–LIZORKIN-TYPE SPACES

2013 ◽  
Vol 11 (05) ◽  
pp. 1350021 ◽  
Author(s):  
DACHUN YANG ◽  
WEN YUAN ◽  
CIQIANG ZHUO
Keyword(s):  
Morrey Spaces ◽  
Schwartz Space ◽  
Complex Interpolation ◽  
Schwartz Functions ◽  
Type Spaces ◽  
Besov Type Spaces

Let θ ∈ (0, 1), s0, s1 ∈ ℝ, τ0, τ1 ∈ [0, ∞), p0, p1 ∈ (0, ∞), q0, q1 ∈ (0, ∞], s = s0(1 - θ) + s1θ, τ = τ0(1-θ) + τ1θ, [Formula: see text] and [Formula: see text]. In this paper, under the restriction [Formula: see text], the authors establish the complex interpolation, on Triebel–Lizorkin-type spaces, that [Formula: see text], where [Formula: see text] denotes the closure of the Schwartz functions in [Formula: see text]. Similar results on Besov-type spaces and Besov–Morrey spaces are also presented. As a corollary, the authors obtain the complex interpolation for Morrey spaces that, for all 1 < p0 ≤ u0 < ∞, 1 < p1 ≤ u1 < ∞ and 1 < p ≤ u < ∞ such that [Formula: see text], [Formula: see text] and p0u1 = p1u0, [Formula: see text], where [Formula: see text] denotes the closure of the Schwartz space in [Formula: see text]. It is known that, if p0u1 ≠ p1u0, these conclusions on Morrey spaces may not be true.

Corrigendum on ``Interpolating sequences on analytic Besov type spaces\"

2010 ◽  
Vol 59 (6) ◽  
pp. 1931-1934 ◽  
Author(s):  
Jordi Pau ◽  
Nicola Arcozzi ◽  
Daniel Blasi
Keyword(s):  
Interpolating Sequences ◽  
Type Spaces ◽  
Besov Type Spaces

scholarly journals Generalized weighted Besov spaces on the Bessel hypergroup

2006 ◽  
Vol 4 (1) ◽  
pp. 91-111
Author(s):  
Miloud Assal ◽  
Hacen Ben Abdallah
Keyword(s):  
Besov Spaces ◽  
Generalized Convolution ◽  
Smooth Functions ◽  
General Properties ◽  
Generalized Translation ◽  
Discrete Norm ◽  
Type Spaces ◽  
Translation Operators ◽  
Weighted Besov Spaces ◽  
Besov Type Spaces

In this paper we study generalized weighted Besov type spaces on the Bessel-Kingman hypergroup. We give different characterizations of these spaces in terms of generalized convolution with a kind of smooth functions and by means of generalized translation operators. Also a discrete norm is given to obtain more general properties on these spaces.

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