Geodesic
A potential theoretic inequality
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 1, pp. 55-65

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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.
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.
Classification : 31B10, 35B45, 35B65
Keywords: Adams trace inequality; Stummel class; Morrey Spaces 
Ragusa, Maria Alessandra; Zamboni, Pietro. A potential theoretic inequality. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 1, pp. 55-65. http://geodesic.mathdoc.fr/item/CMJ_2001_51_1_a5/
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     volume = {51},
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     zbl = {1079.35507},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2001_51_1_a5/}
}
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[1] D. Adams: Traces of potentials arising from traslation invariant operators. Ann. Scuola Norm. Sup. Pisa 25 (1971), 203–217. | MR

[2] L. Hedberg: On certain convolution inequalities. Proc. Amer. Math. Soc. 36 (1972), 505–510. | DOI | MR

[3] M. Schechter: Spectra of Partial Differential Operators. North Holland, 1986. | MR | Zbl

[4] G. V. Welland: Weighted norm inequalities for fractional integral. Proc. Amer. Math. Soc. 51 (1975), 143–148. | DOI | MR