A class of pairs of weights related to the boundedness of the Fractional Integral Operator between $L^p$ and Lipschitz spaces

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_{γ}

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_{γ}

between

B M O

and Lipschitz integral spaces. For the boundedness between Lipschitz integral spaces we obtain sufficient conditions.

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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 42.1 (2001): 133-152. <http://eudml.org/doc/248807>.

@article{Pradolini2001,
abstract = {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.},
author = {Pradolini, Gladis},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {two-weighted inequalities; fractional integral; weighted Lebesgue spaces; weighted Lipschitz spaces; weighted BMO spaces; fractional integral; two-weighted inequalities; weighted Lipschitz spaces; weighted BMO space},
language = {eng},
number = {1},
pages = {133-152},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A class of pairs of weights related to the boundedness of the Fractional Integral Operator between $L^p$ and Lipschitz spaces},
url = {http://eudml.org/doc/248807},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Pradolini, Gladis
TI - A class of pairs of weights related to the boundedness of the Fractional Integral Operator between $L^p$ and Lipschitz spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 1
SP - 133
EP - 152
AB - 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.
LA - eng
KW - two-weighted inequalities; fractional integral; weighted Lebesgue spaces; weighted Lipschitz spaces; weighted BMO spaces; fractional integral; two-weighted inequalities; weighted Lipschitz spaces; weighted BMO space
UR - http://eudml.org/doc/248807
ER -

References

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Wheeden R., Zygmund A., Measure and Integral. An Introduction to Real Analysis, Marcel Dekker Inc, 1977. Zbl0362.26004 MR0492146

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