Corrigendum to ``Carleson measures associated with families of multilinear operators'' (Studia Math. 211 (2012), 71–94)

AbstractBounded and compact differences of two composition operators acting from the weighted Bergman space $$A^p_\omega $$ A ω p to the Lebesgue space $$L^q_\nu $$ L ν q , where $$0<q<p<\infty $$ 0 < q < p < ∞ and $$\omega $$ ω belongs to the class "Equation missing" of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proofs a new description of q-Carleson measures for $$A^p_\omega $$ A ω p , with $$p>q$$ p > q and "Equation missing", involving pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of q-Carleson measures for the classical weighted Bergman space $$A^p_\alpha $$ A α p with $$-1<\alpha <\infty $$ - 1 < α < ∞ to the setting of doubling weights. The case "Equation missing" is also briefly discussed and an open problem concerning this case is posed.

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Wavelet Frames for Distributions in Anisotropic Besov Spaces

Georgian Mathematical Journal ◽

10.1515/gmj.2005.637 ◽

2005 ◽

Vol 12 (4) ◽

pp. 637-658

Author(s):

Dorothee D. Haroske ◽

Erika Tamási

Keyword(s):

Large Class ◽

Besov Spaces ◽

Studia Math ◽

Wavelet Frames ◽

Anisotropic Besov Spaces ◽

Wavelet Decompositions

Abstract This paper deals with wavelet frames in anisotropic Besov spaces , 𝑠 ∈ ℝ, 0 < 𝑝, 𝑞 ≤ ∞, and 𝑎 = (𝑎1, . . . , 𝑎𝑛) is an anisotropy, with 𝑎𝑖 > 0, 𝑖 = 1, . . . , 𝑛, 𝑎1 + . . . + 𝑎𝑛 = 𝑛. We present sub-atomic and wavelet decompositions for a large class of distributions. To some extent our results can be regarded as anisotropic counterparts of those recently obtained in [Triebel, Studia Math. 154: 59–88, 2003].

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Closed surjective ideals of multilinear operators and interpolation

Banach Journal of Mathematical Analysis ◽

10.1007/s43037-020-00115-5 ◽

2021 ◽

Vol 15 (2) ◽

Author(s):

Antonio Manzano ◽

Pilar Rueda ◽

Enrique A. Sánchez-Pérez

Keyword(s):

Multilinear Operators ◽

Ideals Of Multilinear Operators

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Hardy Spaces for Quasiregular Mappings and Composition Operators

Journal of Geometric Analysis ◽

10.1007/s12220-021-00687-0 ◽

2021 ◽

Author(s):

Tomasz Adamowicz ◽

María J. González

Keyword(s):

Hardy Spaces ◽

Composition Operators ◽

Quasiconformal Mappings ◽

Carleson Measures ◽

Quasiregular Mappings ◽

Classical Setting ◽

Appl Math ◽

Analytic Mappings

AbstractWe define Hardy spaces $${\mathcal {H}}^p$$ H p for quasiregular mappings in the plane, and show that for a particular class of these mappings many of the classical properties that hold in the classical setting of analytic mappings still hold. This particular class of quasiregular mappings can be characterised in terms of composition operators when the symbol is quasiconformal. Relations between Carleson measures and Hardy spaces play an important role in the discussion. This program was initiated and developed for Hardy spaces of quasiconformal mappings by Astala and Koskela in 2011 in their paper $${\mathcal {H}}^p$$ H p -theory for Quasiconformal Mappings (Pure Appl Math Q 7(1):19–50, 2011).

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