Geodesic
Two-weighted estimates for generalized fractional maximal operators on non-homogeneous spaces
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 1, pp. 77-94 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Let $\mu $ be a nonnegative Borel measure on $\mathbb R^d$ satisfying that $\mu (Q)\le l(Q)^n$ for every cube $Q\subset \mathbb R^n$, where $l(Q)$ is the side length of the cube $Q$ and $0
Let $\mu $ be a nonnegative Borel measure on $\mathbb R^d$ satisfying that $\mu (Q)\le l(Q)^n$ for every cube $Q\subset \mathbb R^n$, where $l(Q)$ is the side length of the cube $Q$ and $0$. \endgraf We study the class of pairs of weights related to the boundedness of radial maximal operators of fractional type associated to a Young function $B$ in the context of non-homogeneous spaces related to the measure $\mu $. Our results include two-weighted norm and weak type inequalities and pointwise estimates. Particularly, we give an improvement of a two-weighted result for certain fractional maximal operator proved in W. Wang, C. Tan, Z. Lou (2012).
DOI : 10.21136/CMJ.2018.0337-16
Classification : 42B25
Keywords: non-homogeneous space; generalized fractional operator; weight 
@article{10_21136_CMJ_2018_0337_16,
     author = {Pradolini, Gladis and Recchi, Jorgelina},
     title = {Two-weighted estimates for generalized fractional maximal operators on non-homogeneous spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {77--94},
     year = {2018},
     volume = {68},
     number = {1},
     doi = {10.21136/CMJ.2018.0337-16},
     mrnumber = {3783586},
     zbl = {06861568},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0337-16/}
}
TY  - JOUR
AU  - Pradolini, Gladis
AU  - Recchi, Jorgelina
TI  - Two-weighted estimates for generalized fractional maximal operators on non-homogeneous spaces
JO  - Czechoslovak Mathematical Journal
PY  - 2018
SP  - 77
EP  - 94
VL  - 68
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0337-16/
DO  - 10.21136/CMJ.2018.0337-16
LA  - en
ID  - 10_21136_CMJ_2018_0337_16
ER  - 
%0 Journal Article
%A Pradolini, Gladis
%A Recchi, Jorgelina
%T Two-weighted estimates for generalized fractional maximal operators on non-homogeneous spaces
%J Czechoslovak Mathematical Journal
%D 2018
%P 77-94
%V 68
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0337-16/
%R 10.21136/CMJ.2018.0337-16
%G en
%F 10_21136_CMJ_2018_0337_16
Pradolini, Gladis; Recchi, Jorgelina. Two-weighted estimates for generalized fractional maximal operators on non-homogeneous spaces. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 1, pp. 77-94. doi: 10.21136/CMJ.2018.0337-16

[1] Bernardis, A., Dalmasso, E., Pradolini, G.: Generalized maximal functions and related operators on weighted Musielak-Orlicz spaces. Ann. Acad. Sci. Fenn., Math. 39 (2014), 23-50. | DOI | MR | JFM

[2] Bernardis, A., Hartzstein, S., Pradolini, G.: Weighted inequalities for commutators of fractional integrals on spaces of homogeneous type. J. Math. Anal. Appl. 322 (2006), 825-846. | DOI | MR | JFM

[3] Bernardis, A. L., Lorente, M., Riveros, M. S.: Weighted inequalities for fractional integral operators with kernel satisfying Hörmander type conditions. Math. Inequal. Appl. 14 (2011), 881-895. | DOI | MR | JFM

[4] Bernardis, A. L., Pradolini, G., Lorente, M., Riveros, M. S.: Composition of fractional Orlicz maximal operators and $A_1$-weights on spaces of homogeneous type. Acta Math. Sin., Engl. Ser. 26 (2010), 1509-1518. | DOI | MR | JFM

[5] Cruz-Uribe, D., Fiorenza, A.: The $A_\infty$ property for Young functions and weighted norm inequalities. Houston J. Math. 28 (2002), 169-182. | MR | JFM

[6] Cruz-Uribe, D., Fiorenza, A.: Endpoint estimates and weighted norm inequalities for commutators of fractional integrals. Publ. Mat., Barc. 47 (2003), 103-131. | DOI | MR | JFM

[7] Cruz-Uribe, D., Pérez, C.: On the two-weight problem for singular integral operators. Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 1 (2002), 821-849. | MR | JFM

[8] García-Cuerva, J., Martell, J. M.: Two-weight norm inequalities for maximal operators and fractional integrals on non-homogeneous spaces. Indiana Univ. Math. J. 50 (2001), 1241-1280. | DOI | MR | JFM

[9] Gorosito, O., Pradolini, G., Salinas, O.: Weighted weak-type estimates for multilinear commutators of fractional integrals on spaces of homogeneous type. Acta Math. Sin., Engl. Ser. 23 (2007), 1813-1826. | DOI | MR | JFM

[10] Gorosito, O., Pradolini, G., Salinas, O.: Boundedness of the fractional maximal operator on variable exponent Lebesgue spaces: a short proof. Rev. Unión Mat. Argent. 53 (2012), 25-27. | MR | JFM

[11] Hardy, G. H., Littlewood, J. E., Pólya, G.: Inequalities. Cambridge Mathematical Library, Cambridge University Press, Cambridge (1988). | MR | JFM

[12] Lorente, M., Martell, J. M., Riveros, M. S., Torre, A. de la: Generalized Hörmander's conditions, commutators and weights. J. Math. Anal. Appl. 342 (2008), 1399-1425. | DOI | MR | JFM

[13] Lorente, M., Riveros, M. S., Torre, A. de la: Weighted estimates for singular integral operators satisfying Hörmander's conditions of Young type. J. Fourier Anal. Appl. 11 (2005), 497-509. | DOI | MR | JFM

[14] Mateu, J., Mattila, P., Nicolau, A., Orobitg, J.: BMO for nondoubling measures. Duke Math. J. 102 (2000), 533-565. | DOI | MR | JFM

[15] Meng, Y., Yang, D.: Boundedness of commutators with Lipschitz functions in non-homogeneous spaces. Taiwanese J. Math. 10 (2006), 1443-1464. | DOI | MR | JFM

[16] Nazarov, F., Treil, S., Volberg, A.: Cauchy integral and Calderón-Zygmund operators on nonhomogeneous spaces. Int. Math. Res. Not. 1997 (1997), 703-726. | DOI | MR | JFM

[17] Nazarov, F., Treil, S., Volberg, A.: Weak type estimates and Cotlar inequalities for Calderón-Zygmund operators on nonhomogeneous spaces. Int. Math. Res. Not. 1998 (1998), 463-487. | DOI | MR | JFM

[18] Pérez, C.: Two weighted inequalities for potential and fractional type maximal operators. Indiana Univ. Math. J. 43 (1994), 663-683. | DOI | MR | JFM

[19] Pérez, C.: Weighted norm inequalities for singular integral operators. J. Lond. Math. Soc., II. Ser. 49 (1994), 296-308. | DOI | MR | JFM

[20] Pérez, C.: Endpoint estimates for commutators of singular integral operators. J. Funct. Anal. 128 (1995), 163-185. | DOI | MR | JFM

[21] Pérez, C.: On sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator between weighted $L^p$-spaces with different weights. Proc. Lond. Math. Soc., III. Ser. 71 (1995), 135-157. | DOI | MR | JFM

[22] Pérez, C.: Sharp estimates for commutators of singular integrals via iterations of the Hardy-Littlewood maximal function. J. Fourier Anal. Appl. 3 (1997), 743-756. | DOI | MR | JFM

[23] Pérez, C., Pradolini, G.: Sharp weighted endpoint estimates for commutators of singular integrals. Mich. Math. J. 49 (2001), 23-37. | DOI | MR | JFM

[24] Pradolini, G.: Weighted inequalities and pointwise estimates for the multilinear fractional integral and maximal operators. J. Math. Anal. Appl. 367 (2010), 640-656. | DOI | MR | JFM

[25] Pradolini, G., Salinas, O.: Maximal operators on spaces of homogeneous type. Proc. Am. Math. Soc. 132 (2004), 435-441. | DOI | MR | JFM

[26] Tolsa, X.: BMO, $H^1$, and Calderón-Zygmund operators for non doubling measures. Math. Ann. 319 (2001), 89-149. | DOI | MR | JFM

[27] Yang, D., Yang, D., Hu, G.: The Hardy Space $H^1$ with Non-doubling Measures and Their Applications. Lecture Notes in Mathematics 2084, Springer, Cham (2013). | DOI | MR | JFM

[28] Wang, W., Tan, C., Lou, Z.: A note on weighted norm inequalities for fractional maximal operators with non-doubling measures. Taiwanese J. Math. 16 (2012), 1409-1422. | DOI | MR | JFM

Cité par Sources :