Multilinear Marcinkiewicz-Zygmund Inequalities

Mostrar otras versiones (1)

We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on ℓ r -valued extensions of linear operators. We show that for certain 1 ≤ p, q 1 , ⋯ , q m , r≤ ∞, there is a constant C≥ 0 such that for every bounded multilinear operator T:Lq1(μ1)×⋯×Lqm(μm)→Lp(ν) and functi...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autor principal: Carando, D.
Otros Autores: Mazzitelli, M., Ombrosi, S.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: Birkhauser Boston 2019
Acceso en línea:Registro en Scopus
DOI
Handle
Registro en la Biblioteca Digital
Aporte de:Registro referencial: Solicitar el recurso aquí
Biblioteca Central Dr. Luis F. Leloir (FCEN) de Universidad de Buenos Aires
LEADER 07468caa a22007577a 4500
001 PAPER-17569
003 AR-BaUEN
005 20230518204851.0
008 190410s2019 xx ||||fo|||| 00| 0 eng|d
024 7 |2 scopus  |a 2-s2.0-85029158699 
040 |a Scopus  |b spa  |c AR-BaUEN  |d AR-BaUEN 
100 1 |a Carando, D. 
245 1 0 |a Multilinear Marcinkiewicz-Zygmund Inequalities 
260 |b Birkhauser Boston  |c 2019 
270 1 0 |m Ombrosi, S.; Departamento de Matemática, Universidad Nacional del SurArgentina; email: sombrosi@uns.edu.ar 
506 |2 openaire  |e Política editorial 
504 |a Benea, C., Muscalu, C., Multiple vector valued inequalities via the helicoidal method (2016) Anal. PDE, 9, pp. 1931-1988 
504 |a Benea, C., Muscalu, C., Quasi-Banach valued inequalities via the helicoidal method, , Preprint 
504 |a Bergh, J., Interpolation Spaces (1976) An Introduction. Grund- Lehren Der Mathematischen Wissenschaften, 223. , L o ¨ fstr o ¨ m, J, Springer, Berlin 
504 |a Boas, H., Majorant series (2000) J. Korean Math. Soc., 37 (2), pp. 321-337 
504 |a Bombal, F., Pérez-García, D., Villanueva, I., Multilinear extensions of Grothendieck’s theorem (2004) Quart. J. Math., 55 (4), pp. 441-450 
504 |a Bohnenblust, H.F., Hille, E., On the absolute convergence of Dirichlet series (1931) Ann. Math., 32 (3), pp. 600-622 
504 |a Culiuc, A., Di Plinio, F., Ou, Y., Domination of multilinear singular integrals by positive sparse forms 
504 |a Cruz-Uribe, D., Martell, J.M., Pérez, C., Extrapolation from A ∞ weights and applications (2004) J. Funct. Anal., 213 (2), pp. 412-439 
504 |a Curbera, G., García-Cuerva, J., Martell, J.M., Pérez, C., Extrapolation with weights, rearrangement-invariant function spaces, modular inequalities and applications to singular integrals (2006) Adv. Math., 203, pp. 256-318 
504 |a Davie, A.M., Quotient algebras of uniform algebras (1973) J. London Math. Soc., 7 (2), pp. 31-40 
504 |a Defant, A., Floret, K., (1993) Tensor Norms and Operator Ideals, 176. , North-Holland Mathematics Studies, North-Holland Publishing Co., Amsterdam 
504 |a Defant, A., Junge, M., Best constants and asymptotics of Marcinkiewicz-Zygmund inequalities (1997) Studia Math., 125 (3), pp. 271-287 
504 |a Defant, A., Mastyło, M., Interpolation of Fremlin tensor products and Schur factorization of matrices (2012) J. Funct. Anal., 262, pp. 3981-3999 
504 |a Defant, A., Sevilla-Peris, P., A new multilinear insight on littlewood’s 4/3-inequality (2009) J. Funct. Anal., 256 (5), pp. 1642-1664 
504 |a Di Plinio, F., Ou, Y., Banach-valued multilinear singular integrals, , Preprint, To appear in Indiana Univ. Math. J 
504 |a García-Cuerva, J., Rubio de Francia, J.L., (1985) Weighted Norm Inequalities and Related Topics, 116. , North-Holland Mathematics Studies, North-Holland Publishing Co., Amsterdam 
504 |a Gasch, J., Maligranda, L., On vector-valued inequalities of Marcinkiewicz-Zygmund, Herz and Krivine type (1994) Math. Nachr., 167, pp. 95-129 
504 |a Grafakos, L., Martell, J.M., Extrapolation of weighted norm inequalities for multivariable operators and applications (2004) J. Geom. Anal., 14 (1), pp. 19-46 
504 |a Grafakos, L., Torres, R.H., Multilinear Calderón-Zygmund theory (2002) Adv. Math., 165 (1), pp. 124-164 
504 |a Grafakos, L., Torres, R.H., Maximal operator and weighted norm inequalities for multilinear singular integrals (2002) Indiana Univ. Math. J., 51 (5), pp. 1261-1276 
504 |a Herz, C., Theory of p -spaces with an application to convolution operators (1971) Trans. Am. Math. Soc., 154, pp. 69-82 
504 |a Kaijser, S., Some results in the metric theory of tensor products (1978) Studia Math., 63 (2), pp. 157-170 
504 |a Lerner, A., Ombrosi, S., Pérez, C., Torres, R., Trujillo-González, R., New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory (2009) Adv. Math., 220 (4), pp. 1222-1264 
504 |a Marcinkiewicz, J., Zygmund, A., Quelques inégalités pour les opérations linéaires (1939) Fund. Math., 32, pp. 113-121 
504 |a Pérez, C., Torres, R.H., Sharp maximal function estimates for multilinear singular integrals (2003) Contemp. Math., 320, pp. 323-333 
504 |a Pietsch, A., (1980) Operator Ideals, , North-Holland Publishing Co., Amsterdam 
504 |a Quefflec, H.H., Bohr’s vision of ordinary Dirichlet series; old and new results (1995) J. Anal., 3, pp. 43-60 
520 3 |a We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on ℓ r -valued extensions of linear operators. We show that for certain 1 ≤ p, q 1 , ⋯ , q m , r≤ ∞, there is a constant C≥ 0 such that for every bounded multilinear operator T:Lq1(μ1)×⋯×Lqm(μm)→Lp(ν) and functions {fk11}k1=1n1⊂Lq1(μ1),⋯,{fkmm}km=1nm⊂Lqm(μm), the following inequality holds ∥(∑k1,⋯,km|T(fk11,⋯,fkmm)|r)1/r∥Lp(ν)≤C‖T‖∏i=1m∥(∑ki=1ni|fkii|r)1/r∥Lqi(μi).In some cases we also calculate the best constant C≥ 0 satisfying the previous inequality. We apply these results to obtain weighted vector-valued inequalities for multilinear Calderón-Zygmund operators. © 2017, Springer Science+Business Media, LLC.  |l eng 
536 |a Detalles de la financiación: PIP 11220130100329CO 
536 |a Detalles de la financiación: UBACyT, 20020130100474, PICT 2015-2299 
536 |a Detalles de la financiación: Acknowledgements The authors wish to thank C. Muscalu for his valuable comments regarding this work. This project was supported in part by CONICET PIP 11220130100329CO, ANPCyT PICT 2015-2299 and UBACyT 20020130100474. The second author has a postdoctoral position from CONICET. 
593 |a Departamento de Matemática - Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina 
593 |a IMAS-CONICET, Buenos Aires, Argentina 
593 |a Instituto Balseiro, Universidad Nacional de Cuyo - C.N.E.A., Buenos Aires, Argentina 
593 |a Departamento de Matemática, Centro Regional Universitario Bariloche, Universidad Nacional del Comahue, San Carlos de Bariloche, 8400, Argentina 
593 |a Departamento de Matemática, Universidad Nacional del Sur, Bahía Blanca, 8000, Argentina 
593 |a INMABB-CONICET, Bahía Blanca, Argentina 
690 1 0 |a CALDERON-ZYGMUND OPERATORS 
690 1 0 |a MULTILINEAR OPERATORS 
690 1 0 |a VECTOR-VALUED INEQUALITIES 
700 1 |a Mazzitelli, M. 
700 1 |a Ombrosi, S. 
773 0 |d Birkhauser Boston, 2019  |g v. 25  |h pp. 51-85  |k n. 1  |p J. Fourier Anal. Appl.  |x 10695869  |t Journal of Fourier Analysis and Applications 
856 4 1 |u https://www.scopus.com/inward/record.uri?eid=2-s2.0-85029158699&doi=10.1007%2fs00041-017-9563-5&partnerID=40&md5=023c4c60e120eb88bfc8692e55f46b42  |y Registro en Scopus 
856 4 0 |u https://doi.org/10.1007/s00041-017-9563-5  |y DOI 
856 4 0 |u https://hdl.handle.net/20.500.12110/paper_10695869_v25_n1_p51_Carando  |y Handle 
856 4 0 |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10695869_v25_n1_p51_Carando  |y Registro en la Biblioteca Digital 
961 |a paper_10695869_v25_n1_p51_Carando  |b paper  |c PE 
962 |a info:eu-repo/semantics/article  |a info:ar-repo/semantics/artículo  |b info:eu-repo/semantics/publishedVersion 
999 |c 78522 

Ejemplares similares