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010 a| 2023012958;

020 a| 9781470455385q| (paperback);

020 z| 9781470473495q| (pdf);

035 a| (WaSeSS)ssj0002864611;

040 a| LBSORb| engc| LBSORd| WaSeSS;

042 a| pcc;

049 a| EREEa| NEHH;

050 00 a| QA323b| .D66 2023;

082 00 a| 515/.732| 23/eng20230624;

084 a| 46E35a| 46E30a| 46B70a| 42B10a| 42A16a| 26A152| msc;

100 1 a| Domínguez, Óscarq| (Domínguez Bonilla)?| UNAUTHORIZED;

245 10 a| Function spaces of logarithmic smoothnessh| [electronic resource] :b| embeddings and characterizations /c| Óscar Domínguez, Sergey Tikhonov.;

260 a| Providence, RI :b| AMS, American Mathematical Society,c| 2023.;

300 a| vii, 166 pages ;c| 26 cm.;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| volume 282, number 1393;

504 a| Includes bibliographical references (pages157-166).;

505 0 a| Preliminaries -- Embeddings between Besov, Sobolev and Triebel-Lizorkin spaces with logarithmic smoothness -- Characterizations and embedding theorems for general monotone functions -- Characterizations and embedding theorems for lacunary Fourier series -- Optimality of Propositions 1.2 and 1.3 -- Optimality of embeddings between Sobolev and Besov spaces with smoothness close to zero -- Comparison between different kinds of smoothness spaces involving only logarithmic smoothness -- Optimality of embeddings between Besov spaces -- Various characterizations of Besov spaces -- Besov and Bianchini norms -- Functions and their derivatives in Besov spaces -- Lifting operators in Besov spaces -- Regularity estimates of the fractional Laplace operator.;

506 a| Available only to authorized users.;

520 a| "In this paper we present a comprehensive treatment of function spaces with logarithmic smoothness (Besov, Sobolev, Triebel-Lizorkin). We establish the following results: (1) Sharp embeddings between the Besov spaces defined by differences and by Fourier-analytical decompositions as well as between Besov and Sobolev/Triebel-Lizorkin spaces; (2) Various new characterizations for Besov norms in terms of different Kfunctionals. For instance, we derive characterizations via ball averages, approximation methods, heat kernels, and Bianchini-type norms; (3) Sharp estimates for Besov norms of derivatives and potential operators (Riesz and Bessel potentials) in terms of norms of functions themselves. We also obtain quantitative estimates of regularity properties of the fractional Laplacian. The key tools behind our results are limiting interpolation techniques and new characterizations of Besov and Sobolev norms in terms of the behavior of the Fourier transforms for functions such that their Fourier transforms are of monotone type or lacunary series"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Function spaces.=| ^A38116;

650 0 a| Smoothness of functions.=| ^A182188;

650 0 a| Logarithms.=| ^A53305;

650 7 a| Functional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems.2| msc;

650 7 a| Functional analysis -- Linear function spaces and their duals -- Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)2| msc;

650 7 a| Functional analysis -- Normed linear spaces and Banach spaces; Banach lattices -- Interpolation between normed linear spaces.2| msc;

650 7 a| Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type.2| msc;

650 7 a| Harmonic analysis on Euclidean spaces -- Harmonic analysis in one variable -- Fourier coefficients, Fourier series of functions with special properties, special Fourier series.2| msc;

650 7 a| Real functions -- Functions of one variable -- Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.).2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Tikhonov, Sergey,d| 1976-?| UNAUTHORIZED;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=30404205;

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Function spaces of logarithmic smoothness embeddings and characterizations / Óscar Domínguez, Sergey Tikhonov.

Author/creator	Domínguez, Óscar
Other author	Tikhonov, Sergey, 1976-
Format	Electronic
Publication Info	Providence, RI : AMS, American Mathematical Society, 2023.
Description	vii, 166 pages ; 26 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Function spaces. Smoothness of functions. Logarithms.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; volume 282, number 1393
Contents	Preliminaries -- Embeddings between Besov, Sobolev and Triebel-Lizorkin spaces with logarithmic smoothness -- Characterizations and embedding theorems for general monotone functions -- Characterizations and embedding theorems for lacunary Fourier series -- Optimality of Propositions 1.2 and 1.3 -- Optimality of embeddings between Sobolev and Besov spaces with smoothness close to zero -- Comparison between different kinds of smoothness spaces involving only logarithmic smoothness -- Optimality of embeddings between Besov spaces -- Various characterizations of Besov spaces -- Besov and Bianchini norms -- Functions and their derivatives in Besov spaces -- Lifting operators in Besov spaces -- Regularity estimates of the fractional Laplace operator.
Abstract	"In this paper we present a comprehensive treatment of function spaces with logarithmic smoothness (Besov, Sobolev, Triebel-Lizorkin). We establish the following results: (1) Sharp embeddings between the Besov spaces defined by differences and by Fourier-analytical decompositions as well as between Besov and Sobolev/Triebel-Lizorkin spaces; (2) Various new characterizations for Besov norms in terms of different Kfunctionals. For instance, we derive characterizations via ball averages, approximation methods, heat kernels, and Bianchini-type norms; (3) Sharp estimates for Besov norms of derivatives and potential operators (Riesz and Bessel potentials) in terms of norms of functions themselves. We also obtain quantitative estimates of regularity properties of the fractional Laplacian. The key tools behind our results are limiting interpolation techniques and new characterizations of Besov and Sobolev norms in terms of the behavior of the Fourier transforms for functions such that their Fourier transforms are of monotone type or lacunary series"-- Provided by publisher.
Bibliography note	Includes bibliographical references (pages157-166).
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2023012958
ISBN	9781470455385 (paperback)
ISBN	(pdf)

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Function spaces of logarithmic smoothness embeddings and characterizations / Óscar Domínguez, Sergey Tikhonov.

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