Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 20, No. 2, pp. 131-140 (2004)

Translation Invariant Operators on Hardy Spaces over Vilenkin Groups

J.E. Daly and S Fridli

University of Colorado, Eötvös L. University

Abstract: We show that a number of well known multiplier theorems for Hardy spaces over Vilenkin groups follow immediately from a general condition on the kernel of the multiplier operator. In the compact case, this result shows that the multiplier theorems of Kitada, Tateoka, Daly-Phillips, and Simon are best viewed as providing conditions on the partial sums of the Fourier-Vilenkin series of the kernel rather than explicit conditions on the Fourier-Vilenkin coefficients themselves. The theorem is used to prove an extension of the Marcinkiewicz multiplier theorem for Hardy spaces.

Keywords: Convolution operators, Hardy spaces, Vilenkin groups, multipliers.

Classification (MSC2000): 42A45

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