scholarly journals Dyadic Norm Besov-Type Spaces as Trace Spaces on Regular Trees

2019 ◽  
Vol 53 (4) ◽  
pp. 1317-1346 ◽  
Author(s):  
Pekka Koskela ◽  
Zhuang Wang
Keyword(s):  
Sobolev Spaces ◽  
Function Spaces ◽  
First Order ◽  
Type Spaces ◽  
Trace Spaces ◽  
Besov Type Spaces

AbstractIn this paper, we study function spaces defined via dyadic energies on the boundaries of regular trees. We show that correct choices of dyadic energies result in Besov-type spaces that are trace spaces of (weighted) first order Sobolev spaces.

scholarly journals Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces

2017 ◽  
Vol 5 (1) ◽  
pp. 98-115 ◽  
Author(s):  
Eero Saksman ◽  
Tomás Soto
Keyword(s):  
Sobolev Space ◽  
Sobolev Spaces ◽  
Metric Space ◽  
Besov Spaces ◽  
Metric Spaces ◽  
Function Spaces ◽  
First Order ◽  
Trace Theorems ◽  
Euclidean Setting ◽  
Regular Subset

Abstract We establish trace theorems for function spaces defined on general Ahlfors regular metric spaces Z. The results cover the Triebel-Lizorkin spaces and the Besov spaces for smoothness indices s < 1, as well as the first order Hajłasz-Sobolev space M1,p(Z). They generalize the classical results from the Euclidean setting, since the traces of these function spaces onto any closed Ahlfors regular subset F ⊂ Z are Besov spaces defined intrinsically on F. Our method employs the definitions of the function spaces via hyperbolic fillings of the underlying metric space.

Characterization of the function spaces associated with weighted Sobolev spaces of the first order on the real line

2019 ◽  
Vol 74 (6) ◽  
pp. 1075-1115
Author(s):  
D. V. Prokhorov ◽  
V. D. Stepanov ◽  
E. P. Ushakova
Keyword(s):  
Sobolev Spaces ◽  
Real Line ◽  
Weighted Sobolev Spaces ◽  
Function Spaces ◽  
The Real ◽  
First Order

scholarly journals Regularity results for solutions of linear elliptic degenerate boundary-value problems

2020 ◽  
Vol 9 (3) ◽  
pp. 545-566
Author(s):  
A. El Baraka ◽  
M. Masrour
Keyword(s):  
Sobolev Spaces ◽  
General Framework ◽  
A Priori ◽  
A Priori Estimate ◽  
Priori Estimate ◽  
Degenerate Elliptic ◽  
Type Spaces ◽  
Order Degenerate ◽  
Regularity Results ◽  
Besov Type Spaces

Abstract We give an a-priori estimate near the boundary for solutions of a class of higher order degenerate elliptic problems in the general Besov-type spaces $$B^{s,\tau }_{p,q}$$ B p , q s , τ . This paper extends the results found in Hölder spaces $$C^s$$ C s , Sobolev spaces $$H^s$$ H s and Besov spaces $$B^s_{p,q}$$ B p , q s , to the more general framework of Besov-type spaces.

scholarly journals Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces

2016 ◽  
Vol 146 (5) ◽  
pp. 905-927 ◽  
Author(s):  
António Caetano ◽  
Amiran Gogatishvili ◽  
Bohumír Opic
Keyword(s):  
Besov Spaces ◽  
Function Spaces ◽  
Lebesgue Spaces ◽  
Banach Function Spaces ◽  
Compact Embeddings ◽  
Type Spaces ◽  
Besov Type Spaces

There are two main aims of the paper. The first is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second is to extend the criterion for the precompactness of sets in the Lebesgue spaces Lp(ℝn), 1 ⩽ p < ∞, to the so-called power quasi-Banach function spaces. These criteria are applied to establish compact embeddings of abstract Besov spaces into quasi-Banach function spaces. The results are illustrated on embeddings of Besov spaces , into Lorentz-type spaces.

scholarly journals Integral Criteria for Weighted Bloch Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
A. El-Sayed Ahmed ◽  
M. A. Bakhit
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Special Functions ◽  
Function Spaces ◽  
Bloch Functions ◽  
Function Classes ◽  
Type Spaces ◽  
Besov Norms ◽  
Analytic Function Spaces ◽  
Besov Type Spaces

The present manuscript gives analytic characterizations and interesting technique that involves the study of general ϖ -Besov classes of analytic functions by the help of analytic ϖ -Bloch functions. Certain special functions significant in both ϖ -Besov-norms and ϖ -Bloch norms framework and to introduce new important families of analytic classes. Interesting motivation of this concerned paper is to construct some new analytic function classes of general ϖ -Besov-type spaces via integrals on concerned functions view points. The introduced analytic ϖ -Bloch and ϖ -Besov type of functions with some interesting properties for these classes of function spaces are established within the constructions of their norms. Using the defined analytic function spaces, various important relations are also derived.

Characterizations of Besov-Type and Triebel–Lizorkin–Type Spaces via Averages on Balls

2017 ◽  
Vol 60 (3) ◽  
pp. 655-672 ◽  
Author(s):  
Ciqiang Zhuo ◽  
Winfried Sickel ◽  
Dachun Yang ◽  
Wen Yuan
Keyword(s):  
Sobolev Spaces ◽  
Morrey Spaces ◽  
Independent Interest ◽  
Special Cases ◽  
Type Spaces ◽  
Besov Type Spaces

AbstractLet ℓ ∊ ℕ and α > (§, 2ℓ). In this article, the authors establish equivalent characterizations of Besov-type spaces, Triebel–Lizorkin-type spaces, and Besov–Morrey spaces via the sequence {ƒ-Bl,2-kƒ}k consisting of the diòerence between f and the ball average Bl,2-kƒ. These results lead to the introduction of Besov-type spaces, Triebel–Lizorkin-type spaces, and Besov–Morrey spaceswith any positive smoothness order onmetricmeasure spaces. As special cases, the authors obtain a new characterization ofMorrey–Sobolev spaces and Qα spaces with ∈ > (0, 1), which are of independent interest.

scholarly journals Traces of certain classes of holomorphic functions on finite unions of Carleson sequences

1999 ◽  
Vol 41 (1) ◽  
pp. 103-114 ◽  
Author(s):  
ANDREAS HARTMANN
Keyword(s):  
Holomorphic Functions ◽  
Spaces Of Holomorphic Functions ◽  
Hardy Classes ◽  
Type Spaces ◽  
Trace Spaces

We give a method allowing the generalization of the description of trace spaces of certain classes of holomorphic functions on Carleson sequences to finite unions of Carleson sequences. We apply the result to different classes of spaces of holomorphic functions such as Hardy classes and Bergman type spaces.

scholarly journals Besov-type spaces for the Dunkl operator on the real line

2007 ◽  
Vol 199 (1) ◽  
pp. 56-67 ◽  
Author(s):  
Lotfi Kamoun
Keyword(s):  
Real Line ◽  
Dunkl Operator ◽  
The Real ◽  
Type Spaces ◽  
Besov Type Spaces

scholarly journals Density Problems in Sobolev’s Spaces on Time Scales

2021 ◽  
Vol 45 (02) ◽  
pp. 215-223
Author(s):  
AMINE BENAISSA CHERIF ◽  
FATIMA ZOHRA LADRANI
Keyword(s):  
Continuous Function ◽  
Time Scales ◽  
Time Scale ◽  
Function Spaces ◽  
First Order ◽  
Example Spaces

In this paper, we present a generalization of the density some of the functional spaces on the time scale, for example, spaces of rd-continuous function, spaces of Lebesgue Δ-integral and first-order Sobolev’s spaces.

Sign in / Sign up

Export Citation Format

Share Document