Exponential integrability of Riesz potentials of Orlicz functions
نویسندگان
چکیده
منابع مشابه
Hölder 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: Illinois Journal of Mathematics
سال: 2012
ISSN: 0019-2082
DOI: 10.1215/ijm/1385129961