Theory of Function Spaces III

By Hans Triebel. 2008

1,119 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c8a4ffefb3f1c0a4d981a8a74ad5c6171530f225

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Citations in the corpus

The Segal Algebra ${\bf S}_0({\Bbb R}^d)$ and Norm Summability of Fourier Series and Fourier Transforms (2006, background): “For a detailed description of these spaces see Triebel [29], Runst and Sickel [22], Stein [26] and Grafakos [12].”
Relations among Besov-type spaces, Triebel–Lizorkin-type spaces and generalized Carleson measure spaces (2011, background): “A comprehensive treatment of these function spaces and their history can be found in Triebel’s monographes [11, 12].”
VARIABLE BESOV AND TRIEBEL-LIZORKIN SPACES (2008, methodology): “proved to be useful tools in the study of ordinary and partial dierential equations; for details one can see Triebel’s books [ 21 ], [22], [23] and [24] and other literature.”
New properties of Besov and Triebel-Lizorkin spaces on RD-spaces (2009, background): “The results in this paper apply in a wide range of settings, for instance, to Ahlfors n-regular metric measure spaces (see [10]), d-spaces (see [20]), Lie groups of polynomial volume growth (see [21, 15, 1]), (compact) Carnot-Carathéodory (also called sub-Riemannian) manifolds with doubling measures”
Atomic decompositions of function spaces with Muckenhoupt weights, and some relation to fractal analysis (2008, methodology): “Similar to the unweighted case [47] the number N has to be chosen sufficiently large depending on s, p, q and - in our case - r0, see also Theorem 3.”
Spaces of Variable Smoothness and Integrability: Characterizations by Local Means and Ball Means of Differences (2011, methodology): “3 in [52]).”
Local Well-Posedness and Blowup Criterion of the Boussinesq Equations in Critical Besov Spaces (2010, neutral): “[17, 22]).”
Sampling in paley-wiener spaces on combinatorial graphs (2008, background): “S). In the case of Rd such kind inequalities play an important role in harmonic analysis and diﬀerential equations and usually associated with the names of Wirtinger, Poincare, and Sobolev [9], [17], [38]. The following two Lemmas describe some inﬁnite Λ-sets. The ﬁrst Lemma is obvious. Lemma 3.5. S”
Continuous Characterizations of Besov-Lizorkin-Triebel Spaces and New Interpretations as Coorbits (2010, background): “(i) Since the analyzing function or atom g can be chosen arbitrarily we allow more flexibility here than in the results given in Frazier/Jawerth [12] and Triebel [30, 31].”