Product BMO, Little BMO, and Riesz Commutators in the Bessel Setting
نویسندگان
چکیده
منابع مشابه
A Characterization of Product BMO by Commutators
Here R+ denotes the upper half-plane and BMO(R 2 +×R 2 +) is defined to be the dual of the realvariable Hardy space H on the product domain R+×R 2 +. There are several equivalent ways to define this latter space and the reader is referred to [5] for the various characterizations. We will be more interested in the biholomorphic analogue of H, which can be defined in terms of the boundary values ...
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A dx. Given a Banach space (X, ‖ · ‖) and 1 ≤ p < ∞ we shall denote by L(R, X) the space of Bochner p-integrable functions endowed with the norm ‖f‖Lp(Rn,X) = ( ∫ Rn ‖f(x)‖ dx), by Lc (R , X) the closure of the compactly supported functions in L(R, X) and by Lweak,α(R , X) the space of measurable functions such that |{x ∈ R : ‖f(x)‖ > λ}| ≤ α(λ) where α : R → R is a non increasing function. We ...
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Let Mb denote the operation of multiplication by b. Let Hj denote the Hilbert transform performed in the jth coordinate, for j = 1, 2, . . .. Consider the jth order iterated commutator Cb,j = [H1, · · · , [Hj , Mb] · · · ], j = 1, 2, . . . We show that the operator norm of Cb,3 on L (R) is comparable to the norm of b in Chang–Fefferman product BMO(⊗31R 2 +). This fact has some well known equiva...
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Let T be the unit circle on R2. Denote by BMO(T) the classical BMO space and denote by BMOD(T) the usual dyadic BMO space on T. Then, for suitably chosen δ ∈R, we have ‖φ‖BMO(T) ‖φ‖BMOD(T) + ‖φ(· − 2δπ)‖BMOD(T), ∀φ ∈ BMO(T). To cite this article: T. Mei, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 2003 Académie des sciences. Published by Éditions scientifiques et médicales Elsevier SAS. All ri...
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H(⊗1 C+) denotes the Hardy space of square integrable functions analytic in each variable separately. Let P be the natural projection of L(⊗1 C+) onto H (⊗1 C+). A Hankel operator with symbol b is the linear operator from H(⊗1 C+) to H (⊗1 C+) given by Hb φ = P⊖bφ. We show that ‖Hb‖ ≃ ‖P b‖BMO(⊗n 1 C+) , where the right hand norm is S.-Y. Chang and R. Fefferman product BMO. This fact has well k...
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ژورنال
عنوان ژورنال: The Journal of Geometric Analysis
سال: 2017
ISSN: 1050-6926,1559-002X
DOI: 10.1007/s12220-017-9920-2