scholarly journals Real Interpolation of Hardy-Type Spaces and BMO-Regularity

2020 ◽  
Vol 26 (4) ◽  
Author(s):  
Dmitry V. Rutsky
Keyword(s):  
Real Interpolation ◽  
Hardy Type ◽  
Type Spaces

The supremum-involving Hardy-type operators on Lorentz-type spaces

2020 ◽  
Vol 77 (1) ◽  
pp. 1-29
Author(s):  
Qinxiu Sun ◽  
Xiao Yu ◽  
Hongliang Li
Keyword(s):  
Hardy Type ◽  
Type Spaces ◽  
Hardy Type Operators

Atomic hardy-type spaces between H 1 and L 1 on metric spaces with non-doubling measures

2011 ◽  
Vol 27 (12) ◽  
pp. 2445-2468 ◽  
Author(s):  
Li Guang Liu ◽  
Da Chun Yang ◽  
Dong Yong Yang
Keyword(s):  
Metric Spaces ◽  
Hardy Type ◽  
Type Spaces ◽  
Doubling Measures

scholarly journals Interpolation for intersections of Hardy-type spaces

2020 ◽  
Vol 239 (1) ◽  
pp. 21-38
Author(s):  
Sergei V. Kislyakov ◽  
Ilya K. Zlotnikov
Keyword(s):  
Hardy Type ◽  
Type Spaces

scholarly journals Boundedness of Singular Integrals on Hardy Type Spaces Associated with Schrödinger Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Jianfeng Dong ◽  
Jizheng Huang ◽  
Heping Liu
Keyword(s):  
Molecular Characterization ◽  
Singular Integral ◽  
Maximal Function ◽  
Singular Integrals ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Hardy Type ◽  
Type Spaces ◽  
Reverse Hölder

LetL=-Δ+Vbe a Schrödinger operator onRn,n≥3, whereV≢0is a nonnegative potential belonging to the reverse Hölder classBn/2. The Hardy type spacesHLp, n/(n+δ) <p≤1,for someδ>0, are defined in terms of the maximal function with respect to the semigroup{e-tL}t>0. In this paper, we investigate the bounded properties of some singular integral operators related toL, such asLiγand∇L-1/2, on spacesHLp. We give the molecular characterization ofHLp, which is used to establish theHLp-boundedness of singular integrals.

Boundedness and compactness of Hardy-type integral operators on Lorentz-type spaces

2018 ◽  
Vol 30 (4) ◽  
pp. 997-1011 ◽  
Author(s):  
Hongliang Li ◽  
Qinxiu Sun ◽  
Xiao Yu
Keyword(s):  
Banach Spaces ◽  
Measurable Function ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Lorentz Spaces ◽  
Orlicz Functions ◽  
Hardy Type ◽  
Type Integral ◽  
Type Spaces ◽  
Weighted Lorentz Spaces

Abstract Given measurable functions ϕ, ψ on {\mathbb{R}^{+}} and a kernel function {k(x,y)\geq 0} satisfying the Oinarov condition, we study the Hardy operator Kf(x)=\psi(x)\int_{0}^{x}k(x,y)\phi(y)f(y)\,dy,\quad x>0, between Orlicz–Lorentz spaces {\Lambda_{X}^{G}(w)} , where f is a measurable function on {\mathbb{R}^{+}} . We obtain sufficient conditions of boundedness of {K:\Lambda_{u_{0}}^{G_{0}}(w_{0})\rightarrow\Lambda_{u_{1}}^{G_{1}}(w_{1})} and {K:\Lambda_{u_{0}}^{G_{0}}(w_{0})\rightarrow\Lambda_{u_{1}}^{G_{1},\infty}(w_{% 1})} . We also look into boundedness and compactness of {K:\Lambda_{u_{0}}^{p_{0}}(w_{0})\rightarrow\Lambda_{u_{1}}^{p_{1},q_{1}}(w_{1% })} between weighted Lorentz spaces. The function spaces considered here are quasi-Banach spaces rather than Banach spaces. Specializing the weights and the Orlicz functions, we restore the existing results as well as we achieve new results in the new and old settings.

Hardy-Type Operators in Lorentz-Type Spaces Defined on Measure Spaces

2020 ◽  
Vol 51 (3) ◽  
pp. 1105-1132
Author(s):  
Qinxiu Sun ◽  
Xiao Yu ◽  
Hongliang Li
Keyword(s):  
Hardy Type ◽  
Measure Spaces ◽  
Type Spaces ◽  
Hardy Type Operators
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