# Two weight norm inequalities for fractional one-sided maximal and integral operators

Commentationes Mathematicae Universitatis Carolinae (2006)

- Volume: 47, Issue: 1, page 35-46
- ISSN: 0010-2628

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topDe Rosa, Liliana. "Two weight norm inequalities for fractional one-sided maximal and integral operators." Commentationes Mathematicae Universitatis Carolinae 47.1 (2006): 35-46. <http://eudml.org/doc/249843>.

@article{DeRosa2006,

abstract = {In this paper, we give a generalization of Fefferman-Stein inequality for the fractional one-sided maximal operator: \[ \int \_\{-\infty \}^\{+\infty \} M\_\{\alpha \}^+(f)(x)^p w(x)\,dx \le A\_p \int \_\{-\infty \}^\{+\infty \} |f(x)|^p M\_\{\alpha p\}^-(w)(x)\,dx, \]
where $0 < \alpha < 1$ and $1 < p < 1/\alpha $. We also obtain a substitute of dual theorem and weighted norm inequalities for the one-sided fractional integral $I_\{\alpha \}^+$.},

author = {De Rosa, Liliana},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {one-sided fractional operators; weighted inequalities; one-sided fractional operators; weighted inequalities},

language = {eng},

number = {1},

pages = {35-46},

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

title = {Two weight norm inequalities for fractional one-sided maximal and integral operators},

url = {http://eudml.org/doc/249843},

volume = {47},

year = {2006},

}

TY - JOUR

AU - De Rosa, Liliana

TI - Two weight norm inequalities for fractional one-sided maximal and integral operators

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2006

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

VL - 47

IS - 1

SP - 35

EP - 46

AB - In this paper, we give a generalization of Fefferman-Stein inequality for the fractional one-sided maximal operator: \[ \int _{-\infty }^{+\infty } M_{\alpha }^+(f)(x)^p w(x)\,dx \le A_p \int _{-\infty }^{+\infty } |f(x)|^p M_{\alpha p}^-(w)(x)\,dx, \]
where $0 < \alpha < 1$ and $1 < p < 1/\alpha $. We also obtain a substitute of dual theorem and weighted norm inequalities for the one-sided fractional integral $I_{\alpha }^+$.

LA - eng

KW - one-sided fractional operators; weighted inequalities; one-sided fractional operators; weighted inequalities

UR - http://eudml.org/doc/249843

ER -

## References

top- Bennett C., Sharpley R., Interpolation of Operators, Academic Press, New York, 1988. Zbl0647.46057MR0928802
- Cruz-Uribe D., New proofs of two-weight norm inequalities for the maximal operator, Georgian Math. J. 7 1 (2000), 33-42. (2000) Zbl0987.42019MR1768043
- Fefferman C., Stein E.M., Some maximal inequalities, Amer. J. Math. 93 (1971), 107-115. (1971) Zbl0222.26019MR0284802
- García-Cuerva J., Rubio de Francia J.L., Weighted Norm Inequalities and Related Topics, North-Holland, Amsterdam, 1985. MR0848147
- Martín-Reyes F.J., New proofs of weighted inequalities for the one-sided Hardy-Littlewood maximal functions, Proc. Amer. Math. Soc. 117 3 (1993), 691-698. (1993) MR1111435
- Martín-Reyes F.J., Pick L., de la Torre A., ${A}_{\infty}^{+}$ condition, Canad. J. Math. 45 6 (1993), 1231-1244. (1993) MR1247544
- Martín-Reyes F.J., de la Torre A., Two weight norm inequalities for fractional one-sided maximal operators,, Proc. Amer. Math. Soc. 117 2 (1993), 483-489. (1993) MR1110548
- Pérez C., Banach function spaces and the two-weight problem for maximal functions, Proceedings of the Conference on Function Spaces, Differential Operators and Nonlinear Analysis, Paseky nad Jizerou, (1995), pp.141-158. MR1480935
- Riveros M.S., de Rosa L., de la Torre A., Sufficient conditions for one-sided operators, J. Fourier Anal. Appl. 6 6 (2000), 607-621. (2000) Zbl0984.42010MR1790246
- Sawyer E., Weighted inequalities for the one-sided Hardy-Littlewood maximal functions, Trans. Amer. Math. Soc. 297 1 (1986), 53-61. (1986) Zbl0627.42009MR0849466

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