Translation Invariant Operators on Hardy Spaces over Vilenkin Groups
نویسنده
چکیده
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 [6], Tateoka [13], Daly-Phillips [2], and Simon [11] 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.
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