Riemann-Stieltjes operators between α -Bloch spaces and Besov spaces

2009 ◽  
Vol 282 (6) ◽  
pp. 899-911 ◽  
Author(s):  
Songxiao Li ◽  
Stevo Stević
Keyword(s):  
Besov Spaces ◽  
Bloch Spaces

A NEW ESSENTIAL NORM ESTIMATE OF COMPOSITION OPERATORS FROM α-BLOCH SPACES INTO μ-BLOCH SPACES

2013 ◽  
Vol 24 (14) ◽  
pp. 1350104 ◽  
Author(s):  
JULIO C. RAMOS-FERNÁNDEZ
Keyword(s):  
Weight Function ◽  
Unit Disk ◽  
Composition Operator ◽  
Besov Spaces ◽  
Special Function ◽  
Composition Operators ◽  
Bloch Space ◽  
Essential Norm ◽  
Bloch Spaces ◽  
Norm Estimate

Let μ be any weight function defined on the unit disk 𝔻 and let ϕ be an analytic self-map of 𝔻. In this paper, we show that the essential norm of composition operator Cϕ mapping from the α-Bloch space, with α > 0, to μ-Bloch space [Formula: see text] is comparable to [Formula: see text] where, for a ∈ 𝔻, σa is a certain special function in α-Bloch space. As a consequence of our estimate, we extend recent results, about the compactness of composition operators, due to Tjani in [Compact composition operators on Besov spaces, Trans. Amer. Math. Soc.355(11) (2003) 4683–4698] and Malavé Ramírez and Ramos-Fernández in [On a criterion for continuity and compactness of composition operators acting on α-Bloch spaces, C. R. Math. Acad. Sci. Paris351 (2013) 23–26, http://dx.doi.org/10.1016/j.crma.2012.11.013 ].

scholarly journals Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces

2021 ◽  
Vol 11 (1) ◽  
pp. 72-95
Author(s):  
Xiao Zhang ◽  
Feng Liu ◽  
Huiyun Zhang
Keyword(s):  
Hilbert Transform ◽  
Besov Spaces ◽  
Singular Integrals ◽  
Riesz Transform ◽  
Morrey Spaces ◽  
Riesz Transforms ◽  
Rough Kernels ◽  
Lebesgue Spaces ◽  
Variation Operators

Abstract This paper is devoted to investigating the boundedness, continuity and compactness for variation operators of singular integrals and their commutators on Morrey spaces and Besov spaces. More precisely, we establish the boundedness for the variation operators of singular integrals with rough kernels Ω ∈ Lq (S n−1) (q > 1) and their commutators on Morrey spaces as well as the compactness for the above commutators on Lebesgue spaces and Morrey spaces. In addition, we present a criterion on the boundedness and continuity for a class of variation operators of singular integrals and their commutators on Besov spaces. As applications, we obtain the boundedness and continuity for the variation operators of Hilbert transform, Hermit Riesz transform, Riesz transforms and rough singular integrals as well as their commutators on Besov spaces.

scholarly journals Trace operators on fractals, entropy and approximation numbers

2011 ◽  
Vol 18 (3) ◽  
pp. 549-575
Author(s):  
Cornelia Schneider
Keyword(s):  
Besov Spaces ◽  
Trace Operator ◽  
Approximation Numbers ◽  
Atomic Decompositions ◽  
Sharp Estimates ◽  
Compact Embeddings ◽  
Trace Space

Abstract First we compute the trace space of Besov spaces – characterized via atomic decompositions – on fractals Γ, for parameters 0 < p < ∞, 0 < q ≤ min(1, p) and s = (n – d)/p. New Besov spaces on fractals are defined via traces for 0 < p, q ≤ ∞, s ≥ (n – d)/p and some embedding assertions are established. We conclude by studying the compactness of the trace operator TrΓ by giving sharp estimates for entropy and approximation numbers of compact embeddings between Besov spaces. Our results on Besov spaces remain valid considering the classical spaces defined via differences. The trace results are used to study traces in Triebel–Lizorkin spaces as well.

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