# A new proof of weighted weak-type inequalities for fractional integrals

Commentationes Mathematicae Universitatis Carolinae (2001)

- Volume: 42, Issue: 3, page 481-485
- ISSN: 0010-2628

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topCruz-Uribe, David. "A new proof of weighted weak-type inequalities for fractional integrals." Commentationes Mathematicae Universitatis Carolinae 42.3 (2001): 481-485. <http://eudml.org/doc/248790>.

@article{Cruz2001,

abstract = {We give a new and simpler proof of a two-weight, weak $(p,p)$ inequality for fractional integrals first proved by Cruz-Uribe and Pérez [4].},

author = {Cruz-Uribe, David},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {weights; weak-type inequalities; fractional integrals; weight; weak-type inequality; Riesz potential; fractional integral},

language = {eng},

number = {3},

pages = {481-485},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {A new proof of weighted weak-type inequalities for fractional integrals},

url = {http://eudml.org/doc/248790},

volume = {42},

year = {2001},

}

TY - JOUR

AU - Cruz-Uribe, David

TI - A new proof of weighted weak-type inequalities for fractional integrals

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2001

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 42

IS - 3

SP - 481

EP - 485

AB - We give a new and simpler proof of a two-weight, weak $(p,p)$ inequality for fractional integrals first proved by Cruz-Uribe and Pérez [4].

LA - eng

KW - weights; weak-type inequalities; fractional integrals; weight; weak-type inequality; Riesz potential; fractional integral

UR - http://eudml.org/doc/248790

ER -

## References

top- Cruz-Uribe D., SFO, New proofs of two-weight norm inequalities for the maximal operator, Georgian Math. J. 7 (2000), 33-42. (2000) MR1768043
- Cruz-Uribe D., SFO, Fiorenza A., The ${A}_{\infty}$ property for Young functions and weighted norm inequalities, Houston J. Math., to appear. MR1876947
- Cruz-Uribe D., SFO, Pérez C., Sharp two-weight, weak-type norm inequalities for singular integral operators, Math. Res. Lett. 6 (1999), 417-428. (1999) MR1713140
- Cruz-Uribe D., SFO, Pérez C., Two-weight, weak-type norm inequalities for fractional integrals, Calderón-Zygmund operators and commutators, Indiana Math. J. 49 (2000), 697-721. (2000) MR1793688
- García-Cuerva J., Rubio de Francia J.L., Weighted Norm Inequalities and Related Topics, North Holland Math. Studies 116, North Holland, Amsterdam, 1985. MR0848147
- Muckenhoupt B., Wheeden R., Weighted norm inequalities for fractional integrals, Trans. Amer. Math. Soc. 192 (1974), 261-274. (1974) Zbl0289.26010MR0340523
- Pérez C., Two weighted inequalities for potential and fractional type maximal operators, Indiana Math. J. 43 (1994), 663-683. (1994) MR1291534
- Sawyer E.T., Weighted norm inequalities for fractional maximal operators, 1980 Seminar on Harmonic Analysis, CMS Conf. Proc. 1, pp.283-309, Amer. Math. Soc., Providence, 1981. Zbl0546.42018MR0670111
- Sawyer E.T., Wheeden R., Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces, Amer. J. Math. 114 (1992), 813-874. (1992) Zbl0783.42011MR1175693

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