可变核Marcinkiewicz积分交换子在Herz型Hardy空间上的有界性

该文研究由可变核Marcinkiewicz 积分和Lip_β (Rⁿ)(0 <β≤ 1)函数生成的交换子μ_{Ω, b}. 证明了当可变核Ω∈L^∞(Rⁿ)×L^r(S^n-1)(r≥1)$时, 交换子μ_{Ω, b}从Herz型Hardy空间到Herz空间的有界性. 同时建立了参数型Marcinkiewicz 积分的交换子μ^ρ_{Ω, b}在Herz型Hardy空间上的有界性.     

Multipliers on the Set of Rademacher Series in Symmetric Spaces

Let E be a symmetric space on [0,1]. Let (,E) be the space of measurable functions f such that fg E for every almost everywhere convergent series g=b _n r _n E, where (r _n) are the Rademacher functions. It was shown that, for a broad class of spaces E, the space (,E) is not order isomorphic to a symmetric space, and we study the conditions under which such an isomorphism exists. We give conditions on E for (,E) to be order isomorphic to L . This includes some classes of Lorentz and Marcinkiewicz spaces. We also study the conditions under which (,E) is order isomorphic to a symmetric space that differs from L . The answer is positive for the Orlicz spaces E=L _q with _q(t)=exp|t|^q-1 and 0相似文献   

Disjointly strictly singular inclusions of symmetric spaces

In this paper, the disjoint strict singularity of inclusions of symmetric spaces of functions on an interval is considered. A condition for the presence of a “gap” between spaces sufficient for the inclusion of one of these spaces into the other to be disjointly strictly singular is found. The condition is stated in terms of fundamental functions of spaces and is exact in a certain sense. In parallel, necessary and sufficient conditions for an inclusion of Lorentz spaces to be disjointly strictly singular (and similar conditions for Marcinkiewicz spaces) are obtained and certain other assertions are proved. Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 3–14, January, 1999.     

参数型Marcinkiewicz积分在齐次Morrey—Herz空间上的有界性

证明了带可变核的参数型Marcinkiewicz积分算子μΩρ在齐次Morrey—Herz空间MKp,qα,λ及其在弱齐次Morrey—Herz空间WMKp,1α,λ上的有界性,拓宽了以往的结果．     

参数型Marcinkiewicz积分在弱Hardy空间上的有界性

考虑参数型Marcinkicwicz积分uΩ^p（f）（x）={∫0^∞｜1/t^p ∫｜x-y｜≤Ω（x-y）/｜x-y｜^（n-p） f（y）dy｜^2 dt/t}^1/2是（H^p,∞,L^p,∞）型的算子（0〈p〈1）,这里核函数Ω是R^n上的零次齐次函数,并且满足L^1-Dini条件。     

关于积域上的粗糙奇异积分算子的一点注记

讨论积域上的奇异积分算子：ＴΩｆ（ｘ,ｙ） ＝ ｐ．ｖ．∫Ｒｎ×ＲｍΩ（ｕ,ｖ）｜ｕ｜ｎ｜ｖ｜ｍ ｆ（ｘ － ｕ,ｙ － ｖ）ｄｕｄｖ的Ｌｐ 有界性,及相应的Ｍａｒｃｉｎｋｉｅｗ ｉｃｚ积分的Ｌ２ 有界性． 其中Ω为类似文［４］中引进的函数类．     

A Note on Rough Parametric Marcinkiewicz Functions

In this note, we obtain sharp L~p estimates of parametric Marcinkiewicz integral operators. Our result resolves a long standing open problem. Also, we present a class of parametric Marcinkiewicz integral operators that are bounded provided that their kernels belong to the sole space L~1(S~(n-1)).     

Rough Marcinkiewicz integrals with mixed homogeneity on product spaces

In this paper, the parabolic Marcinkiewicz integral operators on the product spaces Rm × Rn (m, n≥ 2) are studied. The Lp -boundedness for such operators are established under rather weak size conditions of the kernels, which essentially improve or extend certain previous results.     

On rough Marcinkiewicz integrals along surfaces

In this paper, the authors establish the LP-mapping properties of certain classes of Marcinkiewicz integral operators along surfaces with rough kernels. The results in this paper essentially extend as well as improve previously known results.     

非齐型空间中一类满足Hrmander条件的Marcinkiewicz交换子估计

记μ为R~d上的非负Radon测度,且仅满足对固定的C_0>0和n∈(0,d],及所有的x∈R~d和r>0,μ(B(x,r))≤C_0r~n.作者建立了一类核函数满足H(o|¨)rmander条件的Marcinkiewicz积分与Lip_β(μ)(0<β)函数生成的交换子由L~p(μ)到L~q(μ),由L~p(μ)到Lip_(β-n/p)(μ)及L~(n/β)(μ)到RBMO(μ)有界.部分结论对经典Marcink(?)ewicz积分也是新的.