On weighted inequalities for operators of potential type
Zhao, Shiying
Colloquium Mathematicae, Tome 70 (1996), p. 95-115 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:210331 
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     author = {Shiying Zhao},
     title = {On weighted inequalities for operators of potential type},
     journal = {Colloquium Mathematicae},
     volume = {70},
     year = {1996},
     pages = {95-115},
     zbl = {0833.42010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv69i1p95bwm}
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Zhao, Shiying. On weighted inequalities for operators of potential type. Colloquium Mathematicae, Tome 70 (1996) pp. 95-115. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv69i1p95bwm/

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