This study establishes the boundedness of sublinear operators on block spaces built on Banach function spaces. These results are used to study the boundedness of the Marcinkiewicz integrals, singular integral operator...This study establishes the boundedness of sublinear operators on block spaces built on Banach function spaces. These results are used to study the boundedness of the Marcinkiewicz integrals, singular integral operators and fractional integral operators with homogeneous kernels on block-type spaces.展开更多
We prove some boundedness results for a large class of sublinear operators with rough kernel on the homogeneous Herz spaces where the three main indices are variable exponents.Some known results are extended.
We obtain the boundedness of some integral operators and commutators on homogeneous Herz spaces with three variable exponents K^(˙α(⋅))_(p(⋅),q(⋅)),such as some sublinear operators,the fractional integral and its co...We obtain the boundedness of some integral operators and commutators on homogeneous Herz spaces with three variable exponents K^(˙α(⋅))_(p(⋅),q(⋅)),such as some sublinear operators,the fractional integral and its commutator.展开更多
In 2011,Dekel et al.developed highly geometric Hardy spaces H^(p)(Θ),for the full range 0<p≤1,which are constructed by continuous multi-level ellipsoid coverΘof R^(n) with high anisotropy in the sense that the e...In 2011,Dekel et al.developed highly geometric Hardy spaces H^(p)(Θ),for the full range 0<p≤1,which are constructed by continuous multi-level ellipsoid coverΘof R^(n) with high anisotropy in the sense that the ellipsoids can change shape rapidly from point to point and from level to level.The authors obtain the finite atomic decomposition characterization of Hardy spaces H^(p)(Θ)and as an application,the authors prove that given an admissible triplet(p,q,l)with 1≤q≤∞,if T is a sublinear operator and uniformly bounded elements of some quasi-Banach space B for maps all(p,q,l)-atoms with q<∞(or all continuous(p,q,l)-atoms with q=∞),then T uniquely extends to a bounded sublinear operator from H^(p)(Θ)to B.These results generalize the known results on the anisotropic Hardy spaces of Bownik et al.展开更多
文摘This study establishes the boundedness of sublinear operators on block spaces built on Banach function spaces. These results are used to study the boundedness of the Marcinkiewicz integrals, singular integral operators and fractional integral operators with homogeneous kernels on block-type spaces.
基金Natural Science Foundation of Education Committee of Anhui Province(No.KJ2019A1196)Anhui Provincial Natural Science Foundation(No.1908085MA19)Preresearch Project of the NNSF of China(No.2019yyzrl4).
文摘We prove some boundedness results for a large class of sublinear operators with rough kernel on the homogeneous Herz spaces where the three main indices are variable exponents.Some known results are extended.
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11671397,12071473).
文摘We obtain the boundedness of some integral operators and commutators on homogeneous Herz spaces with three variable exponents K^(˙α(⋅))_(p(⋅),q(⋅)),such as some sublinear operators,the fractional integral and its commutator.
基金Supported by the Xinjiang Training of Innovative Personnel Natural Science Foundation of China(Grant No.2020D01C048)the National Natural Science Foundation of China(Grant No.11861062)。
文摘In 2011,Dekel et al.developed highly geometric Hardy spaces H^(p)(Θ),for the full range 0<p≤1,which are constructed by continuous multi-level ellipsoid coverΘof R^(n) with high anisotropy in the sense that the ellipsoids can change shape rapidly from point to point and from level to level.The authors obtain the finite atomic decomposition characterization of Hardy spaces H^(p)(Θ)and as an application,the authors prove that given an admissible triplet(p,q,l)with 1≤q≤∞,if T is a sublinear operator and uniformly bounded elements of some quasi-Banach space B for maps all(p,q,l)-atoms with q<∞(or all continuous(p,q,l)-atoms with q=∞),then T uniquely extends to a bounded sublinear operator from H^(p)(Θ)to B.These results generalize the known results on the anisotropic Hardy spaces of Bownik et al.
