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Trace and determinant in Jordan-Banach algebras.

Bernard Aupetit, Abdelaziz Maouche (2002)

Publicacions Matemàtiques

Using an appropriate definition of the multiplicity of a spectral value, we introduce a new definition of the trace and determinant of elements with finite spectrum in Jordan-Banach algebras. We first extend a result obtained by J. Zemánek in the associative case, on the connectedness of projections which are close to each other spectrally (Theorem 2.3). Secondly we show that the rank of the Riesz projection associated to a finite-rank element a and a finite subset of its spectrum is equal to the...

Trace inequalities for fractional integrals in grand Lebesgue spaces

Vakhtang Kokilashvili, Alexander Meskhi (2012)

Studia Mathematica

rning the boundedness for fractional maximal and potential operators defined on quasi-metric measure spaces from L p ) , θ ( X , μ ) to L q ) , q θ / p ( X , ν ) (trace inequality), where 1 < p < q < ∞, θ > 0 and μ satisfies the doubling condition in X. The results are new even for Euclidean spaces. For example, from our general results D. Adams-type necessary and sufficient conditions guaranteeing the trace inequality for fractional maximal functions and potentials defined on so-called s-sets in ℝⁿ follow. Trace inequalities...

Trace inequalities for spaces in spectral duality

O. Tikhonov (1993)

Studia Mathematica

Let (A,e) and (V,K) be an order-unit space and a base-norm space in spectral duality, as in noncommutative spectral theory of Alfsen and Shultz. Let t be a norm lower semicontinuous trace on A, and let φ be a nonnegative convex function on ℝ. It is shown that the mapping a → t(φ(a)) is convex on A. Moreover, the mapping is shown to be nondecreasing if so is φ. Some other similar statements concerning traces and real-valued functions are also obtained.

Trace theorem on the Heisenberg group

Hajer Bahouri, Jean-Yves Chemin, Chao-Jiang Xu (2009)

Annales de l’institut Fourier

We prove in this work the trace and trace lifting theorem for Sobolev spaces on the Heisenberg groups for hypersurfaces with characteristics submanifolds.

Trace Theorems for Sobolev Spaces on Lipschitz Domains. Necessary Conditions

Giuseppe Geymonat (2007)

Annales mathématiques Blaise Pascal

A famous theorem of E. Gagliardo gives the characterization of traces for Sobolev spaces W 1 , p Ω for 1 ≤ p &lt; ∞ when Ω ⊂ ℝ N is a Lipschitz domain. The extension of this result to W m , p Ω for m ≥ 2 and 1 &lt; p &lt; ∞ is now well-known when Ω is a smooth domain. The situation is more complicated for polygonal and polyhedral domains since the characterization is given only in terms of local compatibility conditions at the vertices, edges, .... Some recent papers give the characterization for general Lipschitz domains for m=2 in terms of global...

Traces of anisotropic Besov-Lizorkin-Triebel spaces---a complete treatment of the borderline cases

Walter Farkas, Jon Johnsen, Winfried Sickel (2000)

Mathematica Bohemica

Including the previously untreated borderline cases, the trace spaces (in the distributional sense) of the Besov-Lizorkin-Triebel spaces are determined for the anisotropic (or quasi-homogeneous) version of these classes. The ranges of the traces are in all cases shown to be approximation spaces, and these are shown to be different from the usual spaces precisely in the cases previously untreated. To analyse the new spaces, we carry over some real interpolation results as well as the refined Sobolev...

Traces of Besov spaces on fractal h-sets and dichotomy results

António M. Caetano, Dorothee D. Haroske (2015)

Studia Mathematica

We study the existence of traces of Besov spaces on fractal h-sets Γ with a special focus on assumptions necessary for this existence; in other words, we present criteria for the non-existence of traces. In that sense our paper can be regarded as an extension of Bricchi (2004) and a continuation of Caetano (2013). Closely connected with the problem of existence of traces is the notion of dichotomy in function spaces: We can prove that-depending on the function space and the set Γ-there occurs an...

Traces of functions with a dominating mixed derivative in ℝ 3

Jan Vybíral, Winfried Sickel (2007)

Czechoslovak Mathematical Journal

We investigate traces of functions, belonging to a class of functions with dominating mixed smoothness in ℝ 3 , with respect to planes in oblique position. In comparison with the classical theory for isotropic spaces a few new phenomenona occur. We shall present two different approaches. One is based on the use of the Fourier transform and restricted to p = 2 . The other one is applicable in the general case of Besov-Lizorkin-Triebel spaces and based on atomic decompositions.

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