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Espaces BMO, inégalités de Paley et multiplicateurs idempotents

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Lelièvre H.

Studia Mathematica

1997

tom 123

nr 3

249-274

Generalizing the classical BMO spaces defined on the unit circle 𝕋 with vector or scalar values, we define the spaces $BMO_{ψ_{q}}(𝕋)$ and $BMO_{ψ_{q}}(𝕋,B)$, where $ψ_{q}(x) = e^{x^q} -1$ for x ≥ 0 and q ∈ [1,∞[, and where B is a Banach space. Note that $BMO_{ψ_{1}}(𝕋) = BMO(𝕋)$ and $BMO_{ψ_{1}}(𝕋,B) = BMO(𝕋,B)$ by the John-Nirenberg theorem. Firstly, we study a generalization of the classical Paley inequality and improve the Blasco-Pełczyński theorem in the vector case. Secondly, we compute the idempotent multipliers of $BMO_{ψ_{q}}(𝕋)$. Pisier conjectured that the supports of idempotent multipliers of $L^{ψ_{q}}(𝕋)$ form a Boolean algebra generated by the periodic parts and the finite parts for 2 < q < ∞. We confirm this conjecture with $L^{ψ_{q}}(𝕋)$ replaced by $BMO_{ψ_{q}}(𝕋)$.

Ograniczanie wyników

1 Studia Mathematica

1 Lelièvre H.

1 1997

Wyniki wyszukiwania

Espaces BMO, inégalités de Paley et multiplicateurs idempotents