Geodesic
On weighted inequalities for operators of potential type
Colloquium Mathematicum, Tome 69 (1996) no. 1, pp. 95-115

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

In this paper, we discuss a class of weighted inequalities for operators of potential type on homogeneous spaces. We give sufficient conditions for the weak and strong type weighted inequalities sup_{λ>0} λ|{x ∈ X : |T(fdσ)(x)|>λ }|_{ω}^{1/q} ≤ C (∫_{X} |f|^{p}dσ)^{1/p} and (∫_{X} |T(fdσ)|^{q}dω )^{1/q} ≤ C (∫_X |f|^{p}dσ )^{1/p} in the cases of 0 q p ≤ ∞ and 1 ≤ q p ∞, respectively, where T is an operator of potential type, and ω and σ are Borel measures on the homogeneous space X. We show that under certain restrictions on the measures those sufficient conditions are also necessary. A consequence is given for the fractional integrals in Euclidean spaces.
DOI : 10.4064/cm-69-1-95-115
Keywords: fractional maximal functions, operators of potential type, weights, norm inequalities

Shiying Zhao 1

1 
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Shiying Zhao. On weighted inequalities for operators of potential type. Colloquium Mathematicum, Tome 69 (1996) no. 1, pp. 95-115. doi: 10.4064/cm-69-1-95-115

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