scholarly journals Maximal operators, Riesz transforms and Littlewood–Paley functions associated with Bessel operators on BMO

2010 ◽  
Vol 363 (1) ◽  
pp. 310-326 ◽  
Author(s):  
J.J. Betancor ◽  
A. Chicco Ruiz ◽  
J.C. Fariña ◽  
L. Rodríguez-Mesa
Keyword(s):  
Riesz Transforms ◽  
Maximal Operators ◽  
Bessel Operators

scholarly journals Higher order Riesz transforms associated with Bessel operators

2008 ◽  
Vol 46 (2) ◽  
pp. 219-250 ◽  
Author(s):  
Jorge J. Betancor ◽  
Juan C. Fariña ◽  
Teresa Martinez ◽  
Lourdes Rodríguez-Mesa
Keyword(s):  
Higher Order ◽  
Riesz Transforms ◽  
Bessel Operators

Riesz transforms related to Bessel operators

2007 ◽  
Vol 137 (04) ◽  
pp. 701-725 ◽  
Author(s):  
Jorge J. Betancor ◽  
Juan C. C. Fariña ◽  
Dariusz Buraczewski ◽  
Teresa Martínez ◽  
José L. Torrea
Keyword(s):  
Riesz Transforms ◽  
Bessel Operators

scholarly journals Harmonic analysis operators associated with multidimensional Bessel operators

2012 ◽  
Vol 142 (5) ◽  
pp. 945-974 ◽  
Author(s):  
Jorge J. Betancor ◽  
Alejandro J. Castro ◽  
Jezabel Curbelo
Keyword(s):  
Harmonic Analysis ◽  
Maximal Operator ◽  
Weak Type ◽  
Riesz Transforms ◽  
Heat Semigroup ◽  
Strong Type ◽  
Bessel Operators

We establish that the maximal operator and the Littlewood–Paley g-function associated with the heat semigroup defined by multidimensional Bessel operators are of weak type (1, 1). We also prove that Riesz transforms in the multidimensional Bessel setting are of strong type (p, p), for every 1 < p < ∞, and of weak type (1, 1).

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.

Two Weight Characterizations for the Multilinear Local Maximal Operators

2021 ◽  
Vol 41 (2) ◽  
pp. 596-608
Author(s):  
Yali Pan ◽  
Qingying Xue
Keyword(s):  
Maximal Operators
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