On the Integrability of Strong Maximal Functions Corresponding to Different Frames |
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| Authors: | G. Oniani |
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| Affiliation: | (1) A. Tsereteli Kutaisi State University, 55, Queen Tamar St., Kutaisi, 384000, Georgia |
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| Abstract: | For the frame  in  n, let B2()( )(  n) be a family of all n-dimensional rectangles containing x and having edges parallel to the straight lines of , and let MB2() be a maximal operator corresponding to B2(). The main result of the paper is the followingTheorem.For any function fL(1+1n+L)(n) (n 2) there exists a measure preserving and invertible mapping n  nsuch that | (1) |
 | (2) |
.This theorem gives a general solution of M. de Guzmán's problem that was previously studied by various authors. |
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| Keywords: | Strong maximal operator rectangle frame |
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