Acta mathematica scientia,Series B ›› 1997, Vol. 17 ›› Issue (2): 211-218.
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Liu Jianming1, Zheng Weiiing2
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Abstract: Let q > 2,f is measurable function on Rn such that f(x)|x|n(1-2/q) ∈Lq(Rn), then its Fourier transform f can be defined and there exists a constant Aq such that the inequality||f||q ≤ Aq||f|·|n(1-2/q)||q holds.This is the Hardy-Littlewood Theorem. This paper considers the corresponding result for the Fourier-Bessel transform and Fourier-Jacobi transform.It is interesting that we can deal with theses two cases in the same way,and the function corresponding to|x|n is tw(t), where w(t) is the weight,w(t)=t2α+1 for Fourier-Bessel transform,and w(t)=(2 sinh t)2α+1 (2 cosh t)2β+1 for Fourier-Jacobi transform.
Key words: Hardy-Littlewood theorem, Fourier-Jacobi transform, Fourier-Bessel transform
Liu Jianming, Zheng Weiiing. A HARDY-LITTLEWOOD THEOREM FOR WEIGHTED SPACES[J].Acta mathematica scientia,Series B, 1997, 17(2): 211-218.
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