Estimates for some kakeya-typemaximal operators
Fecha
1993Autor
Materia
Abstract
We use an abstract version of a theorem of Kolmogorov-Seliverstov- Paley to obtain sharp L2 estimates for maximal operators of the form: µβ(f(x) = sup –χєsєβ 1/|S| ∫S |f(x - y)| dy. We consider the cases where β is the class of all rectangles in Rn congru- ent to some dilate of [0, 1]n-l x [0, N-1]; the class congruent to dilates of [0, N-1]n-l x [0, 1]; and, in R2, the class of all rectangles with longest side parallel to a particular countable set of directions that include the lacunary and t ...
We use an abstract version of a theorem of Kolmogorov-Seliverstov- Paley to obtain sharp L2 estimates for maximal operators of the form: µβ(f(x) = sup –χєsєβ 1/|S| ∫S |f(x - y)| dy. We consider the cases where β is the class of all rectangles in Rn congru- ent to some dilate of [0, 1]n-l x [0, N-1]; the class congruent to dilates of [0, N-1]n-l x [0, 1]; and, in R2, the class of all rectangles with longest side parallel to a particular countable set of directions that include the lacunary and the uniformly distributed cases. ...
En
Transactions of the American Mathematical Society. Providence. Vol. 335, no. 2 (feb. 1993), p. 667-682.
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