منابع مشابه
Riesz Transform and Riesz Potentials for Dunkl Transform
Analogous of Riesz potentials and Riesz transforms are defined and studied for the Dunkl transform associated with a family of weighted functions that are invariant under a reflection group. The L boundedness of these operators is established in certain cases.
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An analogue to the theory of Riesz potentials and Liouville operators in R for arbitrary fractal d-sets is developed. Corresponding function spaces agree with traces of euclidean Besov spaces on fractals. By means of associated quadratic forms we construct strongly continuous semigroups with Liouville operators as infinitesimal generator. The case of Dirichlet forms is discussed separately. As ...
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In this Note we study the causal (anticausal) generalized Riesz potential of order α:R Cf(R α A)f) of the function f∈S (cf. (I,1;8) and (I,1;9), respectively). The distributional functions R Cf(R α Af) are causal (anticausal) analogues of the α -dimensional potentials in the ultrahyperbolic space defined by Nozaki (cf. [6], p.85). Therefore, we define the generalized causal (anticausal) Riesz d...
متن کاملHölder Continuity of Sobolev Functions and Riesz Potentials
Let v be a distribution on RN with gradient in Lp for some 1 ≤ p <∞ and let γ ∈ (0, 1) if p ≤ N, γ ∈ [1−N/p, 1) if p > N. The main result of this paper states that if |x|(1−γ)p−N ∗ |∇v|p ∈ L∞, then v ∈ C0,γ(RN ). The trivial case p > N and γ = 1−N/p is Morrey’s theorem. An investigation of the condition |x|(1−γ)p−N ∗|∇v|p ∈ L∞ produces other special cases that do not restrict p. Some rely on “u...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 1999
ISSN: 0373-0956
DOI: 10.5802/aif.1720