Hans Triebel (2011)
Banach Center Publications
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The paper deals with dimension-controllable (tractable) embeddings of Besov spaces on n-dimensional cubes into Zygmund spaces. This can be expressed in terms of tractability envelopes.
Yoshihiro Sawano (2010)
Studia Mathematica
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The aim of the present paper is to obtain an inequality of Brézis-Gallouët-Wainger type for Besov-Morrey spaces. We investigate these spaces in a self-contained manner. Also, we verify that our result is sharp.
Loukas Grafakos, Liguang Liu, Diego Maldonado, Dachun Yang
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The multilinear Calderón-Zygmund theory is developed in the setting of RD-spaces which are spaces of homogeneous type equipped with measures satisfying a reverse doubling condition. The multiple-weight multilinear Calderón-Zygmund theory in this context is also developed in this work. The bilinear T1-theorems for Besov and Triebel-Lizorkin spaces in the full range of exponents are among the main results obtained. Multilinear vector-valued T1 type theorems on Lebesgue spaces, Besov spaces,...
Alicja Gąsiorowska (2011)
Banach Center Publications
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We prove asymptotic formulas for the behavior of Gelfand and Kolmogorov numbers of Sobolev embeddings between Besov and Triebel-Lizorkin spaces of radial distributions. Our method works also for Weyl numbers.
Yong Sheng Han (1994)
Revista Matemática Iberoamericana
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In this paper we use the Calderón-Zygmund operator theory to prove a Calderón type reproducing formula associated with a para-accretive function. Using our Calderón-type reproducing formula we introduce a new class of the Besov and Triebel-Lizorkin spaces and prove a Tb theorem for these new spaces.
David R. Adams (1989)
Banach Center Publications
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David E. Edmunds, W. Desmond Evans, Georgi E. Karadzhov (2006)
Revista Matemática Complutense
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Sharp estimates are obtained for the rates of blow up of the norms of embeddings of Besov spaces in Lorentz spaces as the parameters approach critical values.
B. Bordin, D. L. Fernández (1986)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Björn Jaweth (1978)
Studia Mathematica
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Bogdan Bojarski, Piotr Hajłasz (1993)
Studia Mathematica
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We get a class of pointwise inequalities for Sobolev functions. As a corollary we obtain a short proof of Michael-Ziemer’s theorem which states that Sobolev functions can be approximated by functions both in norm and capacity.
Yong-Kum Cho, Joonil Kim (2006)
Studia Mathematica
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As a natural extension of Sobolev spaces, we consider Hardy-Sobolev spaces and establish an atomic decomposition theorem, analogous to the atomic decomposition characterization of Hardy spaces. As an application, we deduce several embedding results for Hardy-Sobolev spaces.
David E. Edmunds, Petr Gurka, Bohumír Opic (2005)
Studia Mathematica
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We establish compact and continuous embeddings for Bessel potential spaces modelled upon generalized Lorentz-Zygmund spaces. The target spaces are either of Lorentz-Zygmund or Hölder type.
Konstantin E. Tikhomirov (2011)
Banach Center Publications
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We consider a problem of intervals raised by I. Ya. Novikov in [Israel Math. Conf. Proc. 5 (1992), 290], which refines the well-known theorem of J. Marcinkiewicz concerning structure of closed sets [A. Zygmund, Trigonometric Series, Vol. I, Ch. IV, Theorem 2.1]. A positive solution to the problem for some specific cases is obtained. As a result, we strengthen the theorem of Marcinkiewicz for generalized Cantor sets.
Yiyu Liang, Dachun Yang, Wen Yuan, Yoshihiro Sawano, Tino Ullrich
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In this paper, the authors propose a new framework under which a theory of generalized Besov-type and Triebel-Lizorkin-type function spaces is developed. Many function spaces appearing in harmonic analysis fall under the scope of this new framework. The boundedness of the Hardy-Littlewood maximal operator or the related vector-valued maximal function on any of these function spaces is not required to construct these generalized scales of smoothness spaces. Instead, a key idea used is...
Eero Saksman, Tomás Soto (2017)
Analysis and Geometry in Metric Spaces
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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...
Hans Triebel (1981)
Mathematische Zeitschrift
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Laković, B. (1986)
Publications de l'Institut Mathématique. Nouvelle Série
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Piotr Hajlasz, Juha Kinnunen (1998)
Revista Matemática Iberoamericana
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We prove that every Sobolev function defined on a metric space coincides with a Hölder continuous function outside a set of small Hausdorff content or capacity. Moreover, the Hölder continuous function can be chosen so that it approximates the given function in the Sobolev norm. This is a generalization of a result of Malý [Ma1] to the Sobolev spaces on metric spaces [H1].
Teresa Radice (2014)
Studia Mathematica
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In this short note we present new integral formulas for the Hessian determinant. We use them for new definitions of Hessian under minimal regularity assumptions. The Hessian becomes a continuous linear functional on a Sobolev space.
Yongsheng Han, Dachun Yang (2003)
Studia Mathematica
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New norms for some distributions on spaces of homogeneous type which include some fractals are introduced. Using inhomogeneous discrete Calderón reproducing formulae and the Plancherel-Pólya inequalities on spaces of homogeneous type, the authors prove that these norms give a new characterization for the Besov and Triebel-Lizorkin spaces with p, q > 1 and can be used to introduce new inhomogeneous Besov and Triebel-Lizorkin spaces with p, q ≤ 1 on spaces of homogeneous type. Moreover,...
Winfried Sickel (1993)
Forum mathematicum
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