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Displaying similar documents to “Spectral multipliers and multiple-parameter structures on the Heisenberg group”

On relations between operators on R^{N}, T^{N} and Z^{N}

P. Auscher, M. Carro (1992)

Studia Mathematica

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We study different discrete versions of maximal operators and g-functions arising from a convolution operator on R. This allows us, in particular, to complete connections with the results of de Leeuw [L] and Kenig and Tomas [KT] in the setting of the groups R^{N}, T^{N} and Z^{N}.

Fourier analysis in several parameters.

Robert Fefferman (1986)

Revista Matemática Iberoamericana

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Clearly, one of the most basic contributions to the fields of real variables, partial differential equations and Fourier analysis in recent times has been the celebrated theorem of Calderón and Zygmund on the boundedness of singular integrals on R [1].

Variants of the Calderón-Zygmund theory for L-spaces.

Anthony Carbery (1986)

Revista Matemática Iberoamericana

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The purposes of this paper may be described as follows: (i) to provide a useful substitute for the Cotlar-Stein lemma for Lp-spaces (the orthogonality conditions are replaced by certain fairly weak smoothness asumptions); (ii) to investigate the gap between the Hörmander multiplier theorem and the Littman-McCarthy-Rivière example - just how little regularity is really needed? (iii) to simplify and extend the work of Duoandikoetxea...

A multiplier theorem for H-type groups

Rita Pini (1991)

Studia Mathematica

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We prove an L p -boundedness result for a convolution operator with rough kernel supported on a hyperplane of a group of Heisenberg type.

Multipliers for Hermite expansions.

Sundaram Thangavelu (1987)

Revista Matemática Iberoamericana

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The aim of this paper is to prove certain multiplier theorems for the Hermite series.

A Marcinkiewicz type multiplier theorem for H¹ spaces on product domains

Michał Wojciechowski (2000)

Studia Mathematica

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It is proved that if m : ℝ d → ℂ satisfies a suitable integral condition of Marcinkiewicz type then m is a Fourier multiplier on the H 1 space on the product domain ℝ d 1 × . . . × ℝ d k . This implies an estimate of the norm N ( m , L p ( ℝ d ) of the multiplier transformation of m on L p ( ℝ d ) as p→1. Precisely we get N ( m , L p ( ℝ d ) ) ≲ ( p - 1 ) - k . This bound is the best possible in general.