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Article

Ragusa, Maria Alessandra ; Zamboni, Pietro
A potential theoretic inequality. (English). Czechoslovak Mathematical Journal, vol. 51 (2001), issue 1, pp. 55-65
MSC: 31B10, 35B45, 35B65 | MR 1814632 | Zbl 1079.35507
Keywords:
Adams trace inequality; Stummel class; Morrey Spaces
Summary:
In this paper is proved a weighted inequality for Riesz potential similar to the classical one by D. Adams. Here the gain of integrability is not always algebraic, as in the classical case, but depends on the growth properties of a certain function measuring some local potential of the weight.
References:
[1] D. Adams: Traces of potentials arising from traslation invariant operators. Ann. Scuola Norm. Sup. Pisa 25 (1971), 203–217. MR 0287301
[2] L. Hedberg: On certain convolution inequalities. Proc. Amer. Math. Soc. 36 (1972), 505–510. DOI 10.1090/S0002-9939-1972-0312232-4 | MR 0312232
[3] M. Schechter: Spectra of Partial Differential Operators. North Holland, 1986. MR 0869254 | Zbl 0607.35005
[4] G. V. Welland: Weighted norm inequalities for fractional integral. Proc. Amer. Math. Soc. 51 (1975), 143–148. DOI 10.1090/S0002-9939-1975-0369641-X | MR 0369641
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