On the influence of parameters determining anisotropic spaces of smooth functions on characteristics of the embedding theorems

1996 ◽  
Vol 78 (2) ◽  
pp. 142-180
Author(s):  
V. P. Il'in
Keyword(s):  
Embedding Theorems ◽  
Smooth Functions ◽  
Anisotropic Spaces

EMBEDDING THEOREMS FOR CERTAIN ANISOTROPIC BESOV–MORREY SPACES

2010 ◽  
Vol 07 (08) ◽  
pp. 1371-1384 ◽  
Author(s):  
SHABAN KHIDR ◽  
KHALEAL YEIHIA
Keyword(s):  
Bounded Domain ◽  
Morrey Spaces ◽  
Function Spaces ◽  
Integral Representations ◽  
Embedding Theorems ◽  
Smooth Functions

For smooth functions defined on a bounded domain satisfying the weak σ-horn condition, integral representations in terms of their derivatives and their differences are introduced. These representations are employed to prove embedding theorems in the [Formula: see text]-function spaces, [Formula: see text] with [Formula: see text] for all i = 0, 1, 2, …, n and j = 1, 2, …, n.

On a class of weighted Sobolev spaces and the minimization of quadratic forms

1978 ◽  
Vol 81 (1-2) ◽  
pp. 119-130
Author(s):  
Frans Penning ◽  
Niko Sauer
Keyword(s):  
Weight Function ◽  
Sobolev Spaces ◽  
Compact Support ◽  
Quadratic Forms ◽  
Weighted Sobolev Spaces ◽  
Weight Functions ◽  
Compact Embedding ◽  
Embedding Theorems ◽  
Smooth Functions ◽  
Square Integrability

SynopsisIn this paper a class of weighted Sobolev spaces defined in terms of square integrability of the gradient multiplied by a weight function, is studied. The domain of integration is either the spaceRnor a half-space ofRn. Conditions on the weight functions that will ensure density of classes of smooth functions or functions with compact support, and compact embedding theorems, are derived. Finally the results are applied to a class of isoperimetrical problems in the calculus of variations in which the domain of integration is unbounded.

There is no local unconditional structure in anisotropic spaces of smooth functions

1989 ◽  
Vol 29 (3) ◽  
pp. 384-394
Author(s):  
S. V. Kislyakov ◽  
N. G. Sidorenko
Keyword(s):  
Smooth Functions ◽  
Anisotropic Spaces

scholarly journals The embedding theorems for anisotropic Nikol’skii-Besov spaces with generalized mixed smoothness

2021 ◽  
Vol 104 (4) ◽  
pp. 28-34
Author(s):  
K.A. Bekmaganbetov ◽  
◽  
K.Ye. Kervenev ◽  
Ye. Toleugazy ◽  
◽  
...  
Keyword(s):  
Approximation Theory ◽  
Mathematical Physics ◽  
Trigonometric Polynomials ◽  
Embedding Theorems ◽  
Lebesgue Spaces ◽  
Differentiable Functions ◽  
Generalized Mixed Smoothness ◽  
Anisotropic Spaces ◽  
Mixed Metric ◽  
Mixed Smoothness

The theory of embedding of spaces of differentiable functions studies the important relations of differential (smoothness) properties of functions in various metrics and has a wide application in the theory of boundary value problems of mathematical physics, approximation theory, and other fields of mathematics. In this article, we prove the embedding theorems for anisotropic spaces Nikol’skii-Besov with a generalized mixed smoothness and mixed metric, and anisotropic Lorentz spaces. The proofs of the obtained results are based on the inequality of different metrics for trigonometric polynomials in Lebesgue spaces with mixed metrics and interpolation properties of the corresponding spaces.

Approximation properties of repeated de la Vallée-Poussin means for piecewise smooth functions

2017 ◽  
Vol 60 (3) ◽  
pp. 695-713
Author(s):  
I. I. Sharapudinov ◽  
T. I. Sharapudinov ◽  
M. G. Magomed-Kasumov
Keyword(s):  
Piecewise Smooth ◽  
Approximation Properties ◽  
Smooth Functions ◽  
Piecewise Smooth Functions

Sobolev Spaces

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Sobolev Spaces ◽  
Embedding Theorems ◽  
Approximation Numbers ◽  
Selection Of

This chapter presents a selection of some of the most important results in the theory of Sobolev spacesn. Special emphasis is placed on embedding theorems and the question as to whether an embedding map is compact or not. Some results concerning the k-set contraction nature of certain embedding maps are given, for both bounded and unbounded space domains: also the approximation numbers of embedding maps are estimated and these estimates used to classify the embeddings.

Embedding theorems for Janelidze's matrix conditions

2020 ◽  
Vol 224 (2) ◽  
pp. 469-506 ◽  
Author(s):  
Pierre-Alain Jacqmin
Keyword(s):  
Embedding Theorems

scholarly journals Embedding Theorems and Area Operators on Bergman Spaces with Doubling Measure

2021 ◽  
Vol 15 (3) ◽  
Author(s):  
Changbao Pang ◽  
Antti Perälä ◽  
Maofa Wang
Keyword(s):  
Borel Measure ◽  
Bergman Spaces ◽  
Embedding Theorem ◽  
Weighted Bergman Spaces ◽  
Embedding Theorems ◽  
Positive Borel Measure ◽  
Doubling Property ◽  
Area Operator ◽  
Special Cases ◽  
Upper Half Plane

AbstractWe establish an embedding theorem for the weighted Bergman spaces induced by a positive Borel measure $$d\omega (y)dx$$ d ω ( y ) d x with the doubling property $$\omega (0,2t)\le C\omega (0,t)$$ ω ( 0 , 2 t ) ≤ C ω ( 0 , t ) . The characterization is given in terms of Carleson squares on the upper half-plane. As special cases, our result covers the standard weights and logarithmic weights. As an application, we also establish the boundedness of the area operator.

scholarly journals Heterogeneous Urban Exposures and Prevalent Hypertension in the Helsinki Capital Region, Finland

2021 ◽  
Vol 18 (3) ◽  
pp. 1196
Author(s):  
Enembe O. Okokon ◽  
Tarja Yli-Tuomi ◽  
Taina Siponen ◽  
Pekka Tiittanen ◽  
Anu W. Turunen ◽  
...  
Keyword(s):  
Antihypertensive Medication ◽  
Green Space ◽  
Road Traffic ◽  
Traffic Noise ◽  
Fine Particulate Matter ◽  
Binary Logistic Regression ◽  
Wood Smoke ◽  
Road Traffic Noise ◽  
Smooth Functions ◽  
Capital Region

Urban dwellers are simultaneously exposed to several environmental health risk factors. This study aimed to examine the relationship between long-term exposure to fine particulate matter (PM2.5, diameter < 2.5 µm) of residential-wood-burning and road-traffic origin, road-traffic noise, green space around participants’ homes, and hypertension. In 2015 and 2016, we conducted a survey of residents of the Helsinki Capital Region to determine their perceptions of environmental quality and safety, lifestyles, and health statuses. Recent antihypertensive medication was used as an indicator of current hypertensive illness. Individual-level exposure was estimated by linking residential coordinates with modelled outdoor levels of wood-smoke- and traffic-related PM2.5, road-traffic noise, and coverage of natural spaces. Relationships between exposure and hypertension were modelled using multi-exposure and single-exposure binary logistic regression while taking smooth functions into account. Twenty-eight percent of the participants were current users of antihypertensive medication. The odds ratios (95% confidence interval) for antihypertensive use were 1.12 (0.78–1.57); 0.97 (0.76–1.26); 0.98 (0.93–1.04) and 0.99 (0.94–1.04) for wood-smoke PM2.5, road-traffic PM2.5, road-traffic noise, and coverage of green space, respectively. We found no evidence of an effect of the investigated urban exposures on prevalent hypertension in the Helsinki Capital Region.

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