We prove two pointwise estimates relating some classical maximal and singular integral operators. In particular, these estimates imply well-known rearrangement inequalities, and BLO-norm inequalities
@article{bwmeta1.element.bwnjournal-article-smv138i3p285bwm, author = {A. Lerner}, title = {On pointwise estimates for maximal and singular integral operators}, journal = {Studia Mathematica}, volume = {141}, year = {2000}, pages = {285-291}, zbl = {0947.42011}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv138i3p285bwm} }
Lerner, A. On pointwise estimates for maximal and singular integral operators. Studia Mathematica, Tome 141 (2000) pp. 285-291. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv138i3p285bwm/
[00000] [1] R. J. Bagby and D. S. Kurtz, Covering lemmas and the sharp function, Proc. Amer. Math. Soc. 93 (1985), 291-296. | Zbl 0531.42006
[00001] [2] R. J. Bagby and D. S. Kurtz, A rearranged good λ inequality, Trans. Amer. Math. Soc. 293 (1986), 71-81. | Zbl 0585.42018
[00002] [3] C. Bennett, Another characterization of BLO, Proc. Amer. Math. Soc. 85 (1982), 552-556. | Zbl 0512.42022
[00003] [4] C. Bennett, R. DeVore and R. Sharpley, Weak- and BMO, Ann. of Math. 113 (1981), 601-611.
[00004] [5] C. Bennett and R. Sharpley, Weak-type inequalities for and BMO, in: Proc. Sympos. Pure Math. 35, Amer. Math. Soc., 1979, 201-229. | Zbl 0423.30026
[00005] [6] K. M. Chong and N. M. Rice, Equimeasurable Rearrangements of Functions, Queen's Papers in Pure and Appl. Math. 28, Queen's University, Kingston, Ont., 1971.
[00006] [7] R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 15 (1974), 241-250. | Zbl 0291.44007
[00007] [8] R. R. Coifman and R. Rochberg, Another characterization of BMO, Proc. Amer. Math. Soc. 79 (1980), 249-254. | Zbl 0432.42016
[00008] [9] A. Córdoba and C. Fefferman, A weighted norm inequality for singular integrals, Studia Math. 57 (1976), 97-101.
[00009] [10] C. Fefferman and E. M. Stein, spaces of several variables, Acta Math. 129 (1972), 137-193. | Zbl 0257.46078
[00010] [11] B. Jawerth and A. Torchinsky, Local sharp maximal functions, J. Approx. Theory 43 (1985), 231-270. | Zbl 0565.42009
[00011] [12] F. John, Quasi-isometric mappings, in: Seminari 1962-1963 di Analisi, Algebra, Geometria e Topologia (Roma, 1964), Ediz. Cremonese, Roma, 1965, 462-473.
[00012] [13] M. A. Leckband, Structure results on the maximal Hilbert transform and two-weight norm inequalities, Indiana Univ. Math. J. 34 (1985), 259-275. | Zbl 0586.42010
[00013] [15] A. K. Lerner, On weighted estimates of non-increasing rearrangements, East J. Approx. 4 (1998), 277-290. | Zbl 0947.42012
[00014] [16] S. Spanne, Sur l’interpolation entre les espaces , Ann. Scuola Norm. Sup. Pisa 20 (1966), 625-648. | Zbl 0203.12403
[00015] [17] E. M. Stein, Singular integrals, harmonic functions, and differentiability properties of functions of several variables, in: Proc. Sympos. Pure Math. 10, Amer. Math. Soc., 1967, 316-335.
[00016] [18] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970. | Zbl 0207.13501
[00017] [19] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, 1971. | Zbl 0232.42007
[00018] [20] J.-O. Strömberg, Bounded mean oscillation with Orlicz norms and duality of Hardy spaces, Indiana Univ. Math. J. 28 (1979), 511-544. | Zbl 0429.46016