The Maximal Operator on the Amalgam Space
DOI:
https://doi.org/10.15407/mag19.04.679Ключові слова:
амальгамні простори, максимальний оператор, комутаторАнотація
Ми доводимо обмеженість максимального оператора Харді-Літтлвуда на амальгамних просторах $(L^p,\ell^q)(\mathbb{R}^n)$. Як наслідок, одержуємо обмеженість комутаторів на цих просторах.
Mathematical Subject Classification 2020: 42B25, 43A15, 47B47
Посилання
K. Astala, T. Iwaniec, and G. Martin, Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane, Princeton Mathematical Series, 48, Princeton University Press, 2009. https://doi.org/10.1515/9781400830114
J. Bourgain, M. Mirek, E.M. Stein, and B.A. Wróbel, On dimension-free variational inequalities for averaging operators in $R^d$ , Geom. Funct. Anal. 28 (2018), 58--99. https://doi.org/10.1007/s00039-018-0433-3
J. Bourgain, M. Mirek, E.M. Stein, and B.A. Wróbel, Dimension-free estimates for discrete Hardy-Littlewood averaging operators over the cubes in $ Z^d$, Amer. J. Math. 141 (2019), 857--905. https://doi.org/10.1353/ajm.2019.0023
C. Carton-Lebrun, H.P. Heinig, and S.C. Hofmann, Integral operators on weighted amalgams, Studia Math. 109 (1994), 133--157. https://doi.org/10.4064/sm-109-2-133-157
R.R. Coifman, R. Rochberg, and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. of Math. (2) 103 (1976), 611--635. https://doi.org/10.2307/1970954
J.J.F. Fournier and J. Stewart, Amalgams of $L^p$ and ```$ℓ^q$ , Bull. Amer. Math. Soc. (N.S.) 13 (1985), 1--21. https://doi.org/10.1090/S0273-0979-1985-15350-9
J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Mathematics Studies, 116, Holland Publishing Co., 1985.
H. Gunawan and C. Schwanke, The Hardy-Littlewood maximal operator on discrete Morrey spaces, Mediterr. J. Math. 16, (2019), 24. https://doi.org/10.1007/s00009-018-1277-7
F. Holland, Harmonic analysis on amalgams of $L^p$ and $ℓ^q$, J. London Math. Soc. (2) 10 (1975), 295--305. https://doi.org/10.1112/jlms/s2-10.3.295
S. Lu, Y. Ding, and D. Yan, Singular Integrals and Related Topics, World Scientific, 2007. https://doi.org/10.1142/6428
E.M. Stein, Harmonic analysis: Real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, 43, Princeton University Press, 1993. https://doi.org/10.1515/9781400883929
J. Stewart, Fourier transforms of unbounded measures, Canad. J. Math. 31 (1979), 1281--1292. https://doi.org/10.4153/CJM-1979-106-4
N. Wiener, On the representation of functions by trigonometrical integrals, Math. Z. 24 (1926), 575--616. https://doi.org/10.1007/BF01216799
N. Wiener, Tauberian theorems, Ann. of Math. (2) 33 (1932), 1--100. https://doi.org/10.2307/1968102
