Hardy-Sobolev spaces and Besov spaces with a function parameter

1988 ◽  
pp. 158-170 ◽  
Author(s):  
Fernando Cobos ◽  
Dicesar Lass Fernandez
Keyword(s):  
Sobolev Spaces ◽  
Besov Spaces ◽  
Function Parameter

Approximation based on elliptic splines

2014 ◽  
Vol 12 (05) ◽  
pp. 1461014 ◽  
Author(s):  
Zhuyuan Yang ◽  
Zongwen Yang
Keyword(s):  
Sobolev Spaces ◽  
Besov Spaces ◽  
Fourier Transforms ◽  
Projection Operators ◽  
Order Of Approximation ◽  
B Splines ◽  
Interpolation Operators ◽  
Polynomial Reproducing

In this paper, we study the elliptic splines which include the well-known polyharmonic B-splines. We analyze their Fourier transforms, decay behaviors and polynomial reproducing properties. We also study the order of approximation in Sobolev spaces and consider their characterizations of Besov spaces by the scale projection operators, quasi-interpolation operators and wavelet operators.

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.

scholarly journals Inner Functions in Lipschitz, Besov, and Sobolev Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-26 ◽  
Author(s):  
Daniel Girela ◽  
Cristóbal González ◽  
Miroljub Jevtić
Keyword(s):  
Sobolev Spaces ◽  
Besov Spaces ◽  
Inner Function ◽  
Blaschke Products ◽  
Inner Functions ◽  
Finite Blaschke Products ◽  
The Subject

We study the membership of inner functions in Besov, Lipschitz, and Hardy-Sobolev spaces, finding conditions that enable an inner function to be in one of these spaces. Several results in this direction are given that complement or extend previous works on the subject from different authors. In particular, we prove that the only inner functions in either any of the Hardy-Sobolev spacesHαpwith1/p≤α<∞or any of the Besov spacesBαp,  qwith0<p,q≤∞andα≥1/p, except whenp=∞,α=0, and2<q≤∞or when0<p<∞,q=∞, andα=1/pare finite Blaschke products. Our assertion for the spacesB0∞,q,0<q≤2, follows from the fact that they are included in the spaceVMOA. We prove also that for2<q<∞,VMOAis not contained inB0∞,qand that this space contains infinite Blaschke products. Furthermore, we obtain distinct results for other values ofαrelating the membership of an inner functionIin the spaces under consideration with the distribution of the sequences of preimages{I-1(a)},|a|<1. In addition, we include a section devoted to Blaschke products with zeros in a Stolz angle.

Multiplication dans les espaces de Besov

1977 ◽  
Vol 78 (1-2) ◽  
pp. 113-117 ◽  
Author(s):  
J. L. Zolesio
Keyword(s):  
Sobolev Spaces ◽  
Besov Spaces ◽  
Continuous Mapping

SynopsisLet f, g be two functions of two Besov spaces (or Sobolev spaces), we look for the Besov spaces to which the product f × g belongs so that the multiplication is a continuous mapping.

Real Interpolation of Sobolev Spaces on Subdomains of Rn

1978 ◽  
Vol 30 (01) ◽  
pp. 190-214 ◽  
Author(s):  
R. A. Adams ◽  
J. J. F. Fournier
Keyword(s):  
Sobolev Space ◽  
Fractional Order ◽  
Sobolev Spaces ◽  
Besov Spaces ◽  
Interpolation Method ◽  
A Priori ◽  
Real Interpolation ◽  
Convenient Tool ◽  
Real Interpolation Method ◽  
Nikolskii Spaces

The real interpolation method is a very convenient tool in the study of imbedding relationships among Sobolev spaces and some of their fractional order generalizations, (Besov spaces, Nikolskii spaces etc.) Central to the application of these methods is the a priori determination that a given Sobolev space Wk'p(Ω) belongs to an appropriate class of spaces intermediate between two other “extreme” spaces.

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