Sharp estimates for the nontangential maximal function and the Lusin area function in Lipschitz domains

Authors:
Rodrigo Bañuelos and Charles N. Moore

Journal:
Trans. Amer. Math. Soc. **312** (1989), 641-662

MSC:
Primary 42B25; Secondary 31A20

DOI:
https://doi.org/10.1090/S0002-9947-1989-0957080-4

MathSciNet review:
957080

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Abstract: Let be a harmonic function on a domain of the form where is a Lipschitz function. The authors show a good- inequality between , the Lusin area function of , and , the nontangential maximal function of . This leads to an inequality of the form which is sharp in the sense that is of the smallest possible order in as . For and we also consider the functions and and show that a corollary of the good- inequality is a law of the iterated logarithm involving these two functions as . If and has a small Lipschitz constant the above results are shown valid with the roles of and interchanged.

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DOI:
https://doi.org/10.1090/S0002-9947-1989-0957080-4

Article copyright:
© Copyright 1989
American Mathematical Society