TY - JOUR

T1 - Maximal functions with respect to differential bases measuring mean oscillation

AU - Lerner, A. K.

PY - 1998

Y1 - 1998

N2 - In this paper we study maximal sharp functions associated with arbitrary differential bases. The definition of these functions goes back to the papers by F. John (1965), and by C. Fefferman and E. M. Stein (1972), where the classical bases consisting of cubic intervals were considered. We obtain conditions imposed on the basis, under which inequalities, known earlier in the case of a basis of cubes, are valid for the considered maximal functions. The main results are formulated in terms of nonincreasing rearrangements. In the capacity of applications, we obtain estimates of the rearrangements of subadditive operators acting in BMO. In particular, the estimate for the Hilbert transform, obtained earlier by C. Bennett and K. Rudnick, follows.

AB - In this paper we study maximal sharp functions associated with arbitrary differential bases. The definition of these functions goes back to the papers by F. John (1965), and by C. Fefferman and E. M. Stein (1972), where the classical bases consisting of cubic intervals were considered. We obtain conditions imposed on the basis, under which inequalities, known earlier in the case of a basis of cubes, are valid for the considered maximal functions. The main results are formulated in terms of nonincreasing rearrangements. In the capacity of applications, we obtain estimates of the rearrangements of subadditive operators acting in BMO. In particular, the estimate for the Hilbert transform, obtained earlier by C. Bennett and K. Rudnick, follows.

UR - http://www.scopus.com/inward/record.url?scp=0011968709&partnerID=8YFLogxK

U2 - 10.1007/BF02771073

DO - 10.1007/BF02771073

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AN - SCOPUS:0011968709

SN - 0133-3852

VL - 24

SP - 41

EP - 58

JO - Analysis Mathematica

JF - Analysis Mathematica

IS - 1

ER -