WeightedH p multipliers on locally compact Vilenkin groups
Copyright policy )WeightedH p multipliers on locally compact Vilenkin groups
Let G be a locally compact Vilenkin group. We give a maximal function characterization of the power-weighted (atomic) \(H^ p\) spaces over G, and give a Hörmander type multiplier theorem for these spaces. Hörmander type condition for the multiplier is formulated in terms of the dyadic derivative of fractional order. Our main result is as follows: Theorem. Let \(01/p-1/\max (2,s')\). Then \(\phi\in {\mathcal M}(H^ p_{\alpha})\) if \(\max (-1,-p\lambda)<\alpha \leq 0\).
- Hirosaki University Japan
- DigiZeitschriften Germany
510.mathematics, maximal function, locally compact Vilenkin group, Hörmander type multiplier theorem, dyadic derivative, Analysis on ordered groups, \(H^p\)-theory, \(L^p\)-spaces and other function spaces on groups, semigroups, etc., Analysis on specific locally compact and other abelian groups, Article, Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
510.mathematics, maximal function, locally compact Vilenkin group, Hörmander type multiplier theorem, dyadic derivative, Analysis on ordered groups, \(H^p\)-theory, \(L^p\)-spaces and other function spaces on groups, semigroups, etc., Analysis on specific locally compact and other abelian groups, Article, Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
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