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Radial maximal function characterizations for Hardy spaces on RD-spaces

Loukas Grafakos, Liguang Liu, Dachun Yang (2009)

Bulletin de la Société Mathématique de France

An RD-space 𝒳 is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds. The authors prove that for a space of homogeneous type 𝒳 having “dimension” n , there exists a p 0 ( n / ( n + 1 ) , 1 ) such that for certain classes of distributions, the L p ( 𝒳 ) quasi-norms of their radial maximal functions and grand maximal functions are equivalent when p ( p 0 , ] . This result yields a radial maximal function characterization for Hardy spaces on 𝒳 .

Random perturbations of exponential Riesz bases in L 2 ( - π , π )

Gennadii Chistyakov, Yura Lyubarskii (1997)

Annales de l'institut Fourier

Let a sequence { λ n } be given such that the exponential system { exp ( i λ n x ) } forms a Riesz basis in L 2 ( - π , π ) and { ξ n } be a sequence of independent real-valued random variables. We study the properties of the system { exp ( i ( λ n + ξ n ) x ) } as well as related problems on estimation of entire functions with random zeroes and also problems on reconstruction of bandlimited signals with bandwidth 2 π via their samples at the random points { λ n + ξ n } .

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