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arXiv · 1402.2886

On vector-valued tent spaces and Hardy spaces associated with non-negative self-adjoint operators

Mikko Kemppainen
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Abstract

In this paper we study Hardy spaces associated with non-negative self-adjoint operators and develop their vector-valued theory. The complex interpolation scales of vector-valued tent spaces and Hardy spaces are extended to the endpoint p=1. The holomorphic functional calculus of L is also shown to be bounded on the associated Hardy space H^1_L(X). These results, along with the atomic decomposition for the aforementioned space, rely on boundedness of certain integral operators on the tent space T^1(X).

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Mikko Kemppainen. 2015-08-19. On vector-valued tent spaces and Hardy spaces associated with non-negative self-adjoint operators. https://doi.org/10.1017/s0017089515000415

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