Displaying similar documents to “Almost everywhere convergence of Laguerre series”

L multipliers and their H-L estimates on the Heisenberg group.

Chin-Cheng Lin (1995)

Revista Matemática Iberoamericana

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We give a Hörmander-type sufficient condition on an operator-valued function M that implies the L-boundedness result for the operator T defined by (Tf)^ = Mf^ on the (2n + 1)-dimensional Heisenberg group H. Here ^ denotes the Fourier transform on H defined in terms of the Fock representations. We also show the H-L boundedness of T, ||Tf|| ≤ C||f||, for H under the same hypotheses of L-boundedness.

Almost everywhere summability of Laguerre series. II

K. Stempak (1992)

Studia Mathematica

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Using methods from [9] we prove the almost everywhere convergence of the Cesàro means of Laguerre series associated with the system of Laguerre functions L n a ( x ) = ( n ! / Γ ( n + a + 1 ) ) 1 / 2 e - x / 2 x a / 2 L n a ( x ) , n = 0,1,2,..., a ≥ 0. The novel ingredient we add to our previous technique is the A p weights theory. We also take the opportunity to comment and slightly improve on our results from [9].