A class of pairs of weights related to the boundedness of the Fractional Integral Operator between $L^p$ and Lipschitz spaces
Pradolini, Gladis
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001), p. 133-152 / Harvested from Czech Digital Mathematics Library
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In [P] we characterize the pairs of weights for which the fractional integral operator $I_{\gamma}$ of order $\gamma$ from a weighted Lebesgue space into a suitable weighted $BMO$ and Lipschitz integral space is bounded. In this paper we consider other weighted Lipschitz integral spaces that contain those defined in [P], and we obtain results on pairs of weights related to the boundedness of $I_{\gamma}$ acting from weighted Lebesgue spaces into these spaces. Also, we study the properties of those classes of weights and compare them with the classes given in [P]. Then, under additional assumptions on the weights, we obtain necessary and sufficient conditions for the boundedness of $I_{\gamma}$ between $BMO$ and Lipschitz integral spaces. For the boundedness between Lipschitz integral spaces we obtain sufficient conditions.

Publié le : 2001-01-01
Classification:  42B25,  47B38,  47G10 
@article{119229,
     author = {Gladis Pradolini},
     title = {A class of pairs of weights related to the boundedness of the Fractional Integral Operator between $L^p$ and Lipschitz spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {42},
     year = {2001},
     pages = {133-152},
     zbl = {1055.42015},
     mrnumber = {1825378},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119229}
}

Pradolini, Gladis. A class of pairs of weights related to the boundedness of the Fractional Integral Operator between $L^p$ and Lipschitz spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 133-152. http://gdmltest.u-ga.fr/item/119229/

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