# 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 (2001)

- Volume: 42, Issue: 1, page 133-152
- ISSN: 0010-2628

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topPradolini, 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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- Pradolini G., Two-weighted norm inequalities for the fractional integral operator between ${L}^{p}$ and Lipschitz spaces, to appear in Comment. Math. Polish Acad. Sci. MR1876717
- Sobolev S.L., On a theorem in functional analysis, Math. Sb. 4 (46) (1938), 471-497; English transl.: Amer. Math. Soc. Transl. (2) 34 (1963), 39-68.
- Stein E., Weiss G., Fractional integrals on n-dimensional euclidean space, J. Math. Mech. 7 (1958), 503-514; MR 20#4746. (1958) Zbl0082.27201MR0098285
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## Citations in EuDML Documents

top- Gladis Pradolini, Oscar Salinas, The fractional integral between weighted Orlicz and $BM{O}_{\phi}$ spaces on spaces of homogeneous type
- Gladis Pradolini, Jorgelina Recchi, On optimal parameters involved with two-weighted estimates of commutators of singular and fractional operators with Lipschitz symbols

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