Basis in the big disk algebra and in the corresponding Hardy-space.

F. Lancien

Displaying similar documents to “Basis in the big disk algebra and in the corresponding Hardy-space.”

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Uniqueness of unconditional bases in $c_{0}$ -products

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We give counterexamples to a conjecture of Bourgain, Casazza, Lindenstrauss and Tzafriri that if X has a unique unconditional basis (up to permutation) then so does $c_{0} (X)$ . We also give some positive results including a simpler proof that $c_{0} (ℓ_{1})$ has a unique unconditional basis and a proof that $c_{0} (ℓ_{p_{n}}^{N_{n}})$ has a unique unconditional basis when $p_{n} ￬ 1$ , $N_{n + 1} \geq 2 N_{n}$ and $(p_{n} - p_{n + 1}) l o g N_{n}$ remains bounded.

Extensions of a Fourier multiplier theorem of Paley, II

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A remark on the multipliers of the Haar basis of L¹[0,1]

H. M. Wark (2015)

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A proof of a necessary and sufficient condition for a sequence to be a multiplier of the normalized Haar basis of L¹[0,1] is given. This proof depends only on the most elementary properties of this system and is an alternative proof to that recently found by Semenov & Uksusov (2012). Additionally, representations are given, which use stochastic processes, of this multiplier norm and of related multiplier norms.

Multiplier operators on product spaces

Hung Viet Le (2002)

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The author proves the boundedness for a class of multiplier operators on product spaces. This extends a result obtained by Lung-Kee Chen in 1994.

A Marcinkiewicz type multiplier theorem for H¹ spaces on product domains

Michał Wojciechowski (2000)

Studia Mathematica

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It is proved that if $m : ℝ^{d} \to ℂ$ satisfies a suitable integral condition of Marcinkiewicz type then m is a Fourier multiplier on the $H^{1}$ space on the product domain $ℝ^{d_{1}} \times . . . \times ℝ^{d_{k}}$ . This implies an estimate of the norm $N (m, L^{p} (ℝ^{d})$ of the multiplier transformation of m on $L^{p} (ℝ^{d})$ as p→1. Precisely we get $N (m, L^{p} (ℝ^{d})) ≲ {(p - 1)}^{- k}$ . This bound is the best possible in general.