The Kakeya Maximal Function and the Spherical Summation Multipliers
Copyright policy )The Kakeya Maximal Function and the Spherical Summation Multipliers
obvious cases: n = 1 or p =2; and also Fefferman [4] proved that TX is bounded on L P (Rn) provided that p (X) (n - 1)/4. This result has been sharpened by Tomas [15] to X > (n - 1)/2(n + 1). Finally Carleson and Sjolin [3], Fefferman [6] and Hormander [10] proved that, in R2, TA is bounded on LP whenever X >0 and p(X) 2 we have the natural question: is TX (X >0) bounded on L P(R'), p(X) < p < p'(X)? Our approach to the problem is inspired by the work of Fefferman and it is as follows: The multiplier theorem for TX can be easily reduced to this problem:
Conjugate functions, conjugate series, singular integrals, Summability and absolute summability of Fourier and trigonometric series, Multipliers in one variable harmonic analysis
Conjugate functions, conjugate series, singular integrals, Summability and absolute summability of Fourier and trigonometric series, Multipliers in one variable harmonic analysis
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