Duals of homogeneous weighted sequence Besov spaces and applications

Huang, Po-Kai; Wang, Kunchuan

doi:10.1515/jaa.2011.012

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Diagonal Matrices and Duality1

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“…In order to find the dual space of ḃα,q p,w for 0 < p ≤ 1 and 0 < q ≤ ∞, we need to define a sequence space ċα,q p,w given in [10].…”

Section: Diagonal Matrices and Dualitymentioning

confidence: 99%

Some Operators Acting on Weighted Sequence Besov Spaces and Applications

Huang¹,

Wang²

2012

Taiwanese J. Math.

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In this article, we study the boundedness of matrix operators acting on weighted sequence Besov spaces ḃα,q p,w . First we obtain the necessary and sufficient condition for the boundedness of diagonal matrices acting on weighted sequence Besov space ḃα,q p,w , and investigate the duals of ḃα,q p,w , where the weight is nonnegative and locally integrable. In particular, when 0 < p < 1, we find a type of new sequence sapces which characterize the dual space of ḃα,q p,w . We also use the duals of ḃα,q p,w to characterize an algebra of matrix operators acting on weighted sequence Besov spaces ḃα,q p,w and find the necessary and sufficient conditions to such a characterization. Note that we do not require that the given weight satisfies the doubling condition in this situation.Using these results, we give some applications to characterize the boundedness of Fourier-Haar multipliers and paraproduct operators. In this situation, we need to require that the weight w is an A p weight.

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“…In order to find the dual space of ḃα,q p,w for 0 < p ≤ 1 and 0 < q ≤ ∞, we need to define a sequence space ċα,q p,w given in [10].…”

Section: Diagonal Matrices and Dualitymentioning

confidence: 99%