Geodesic
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) no. 1, pp. 133-152 Cet article a éte moissonné depuis la source 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.
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.
Classification : 42B25, 47B38, 47G10
Keywords: two-weighted inequalities; fractional integral; weighted Lebesgue spaces; \newline weighted Lipschitz spaces; weighted BMO spaces. 
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     author = {Pradolini, Gladis},
     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},
     pages = {133--152},
     year = {2001},
     volume = {42},
     number = {1},
     mrnumber = {1825378},
     zbl = {1055.42015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2001_42_1_a9/}
}
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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) no. 1, pp. 133-152. http://geodesic.mathdoc.fr/item/CMUC_2001_42_1_a9/