Besov spaces and Herz spaces on local fields

1998 ◽  
Vol 41 (10) ◽  
pp. 1051-1060 ◽  
Author(s):  
Yueping Zhu ◽  
Weixing Zheng
Keyword(s):  
Besov Spaces ◽  
Local Fields ◽  
Herz Spaces

scholarly journals The Decomposition of Herz Spaces on Local Fields and Its Applications

1995 ◽  
Vol 196 (1) ◽  
pp. 296-313 ◽  
Author(s):  
S.Z. Lu ◽  
D.C. Yang
Keyword(s):  
Local Fields ◽  
Herz Spaces

scholarly journals Besov spaces on local fields

1989 ◽  
Vol 22 (1) ◽  
pp. 131-136
Author(s):  
J. Franke
Keyword(s):  
Besov Spaces ◽  
Local Fields

Local Fields

1986 ◽  
Author(s):  
J. W. S. Cassels
Keyword(s):  
Local Fields

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 Weighted CBMO estimates for commutators of matrix Hausdorff operator on the Heisenberg group

2020 ◽  
Vol 18 (1) ◽  
pp. 496-511
Author(s):  
Amna Ajaib ◽  
Amjad Hussain
Keyword(s):  
Heisenberg Group ◽  
Herz Spaces ◽  
Hausdorff Operator ◽  
Hausdorff Operators

Abstract In this article, we study the commutators of Hausdorff operators and establish their boundedness on the weighted Herz spaces in the setting of the Heisenberg group.

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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