In this paper, the authors establish the boundedness of multilinear commutators generated by a Marcinkiewicz integral operator and a RBMO（μ） function on homogeneous Morrey-Herz spaces with non doubling measures.
We study the doubling property of binomial measures on generalized ternary Cantor subsets of [0, 1]. We find some new phenomena. There are three different cases. In the first case, we obtain an equivalent condition fo...We study the doubling property of binomial measures on generalized ternary Cantor subsets of [0, 1]. We find some new phenomena. There are three different cases. In the first case, we obtain an equivalent condition for the measure to be doubling. In the other cases, we show that the condition is not necessary. Then facts and partial results are discussed.展开更多
Let μ be a nonnegative Radon measure on Rd which satisfies the polynomial growth condition that there exist positive constants Co and n ∈ （0,d） such that, for all x ∈ Rd and r 〉 0, μ（B（x, r））≤ Corn, where ...Let μ be a nonnegative Radon measure on Rd which satisfies the polynomial growth condition that there exist positive constants Co and n ∈ （0,d） such that, for all x ∈ Rd and r 〉 0, μ（B（x, r））≤ Corn, where B（x, r） denotes the open ball centered at x and having radius r. In this paper, we show that, if μ（Rd） 〈∞, then the boundedness of a Calderdn-Zygmund operator T on L2（μ） is equivalent to that of T from the localized atomic Hardy space h1（μ） to L1,∞（μ） or from h1（μ） to L1（μ）.展开更多
The mulfifractal formalism for single measure is reviewed. Next, a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Ha...The mulfifractal formalism for single measure is reviewed. Next, a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Hausdorff and packing measures to a vector of simultaneously many measures. Borel-Cantelli and Large deviations Theorems are extended to higher orders and thus applied for the validity of the new variant of the multifractal formalism for some special cases of multi-doubling type measures.展开更多
Electronic speckle pattern interferometry（ESPI） and digital speckle pattern interferometry are wellestablished non-contact measurement methods. They have been widely used to carry out precise deformation mapping. Ho...Electronic speckle pattern interferometry（ESPI） and digital speckle pattern interferometry are wellestablished non-contact measurement methods. They have been widely used to carry out precise deformation mapping. However, the simultaneous two-dimensional（2D） or three-dimensional（3D） deformation measurements using ESPI with phase shifting usually involve complicated and slow equipment. In this Letter, we solve these issues by proposing a modified ESPI system based on double phase modulations with only one laser and one camera. In-plane normal and shear strains are obtained with good quality. This system can also be developed to measure 3D deformation, and it has the potential to carry out faster measurements with a highspeed camera.展开更多
We survey some recent progress in the study of stability of elliptic Harnack inequalities under form-bounded perturbations for strongly local Dirichlet forms on complete locally compact separable metric spaces.
Civen two doubling measures μ and v in a metric apace (S.p)of homogeneous type. let B_0 S be a given ball. It has been a well-known result bv now (see)[1 4])theat the validity of an L^1→L^1 Poincaré inequality ...Civen two doubling measures μ and v in a metric apace (S.p)of homogeneous type. let B_0 S be a given ball. It has been a well-known result bv now (see)[1 4])theat the validity of an L^1→L^1 Poincaré inequality of the following form: f_B|f-f_B|dv≤cr(B)f_Bgdμ. for all metric balls B B_0 S, implies a variant of representation formula of fractonal integral type: |f(x)-f_(B(11))|≤C integral from n=B_(11) g(y)p(x, y)/μ(B(x, p(x, y)))dμ(y)+C(r(B_0))/(μ(B_0))integral from n=B_0 g(y)dμ(y). One of the main results of this paper shows that an L^1 to L^q Poincaré inequality for some 01, i.e.. (f_B|f-f_B|~q dv)^(1/q)≤cr(B) f_B gdμ, for all metric balls B B_0. will suffice to imply the above representation formula. As an immediate corollary, we can show that the weak-type condition. sup_(λ>0)(λv({x ∈ B:|f(x)-f_B|>λ}))/v(B)≤Gr (B)f_B gdμ. also implies the same formula. Analogous theorems related to high-order Poincaréinequalities and Sobolev spaces in metric spaces are also proved.展开更多
In this paper,we compare the mutual multifractal Renyi dimensions to the´mutual multifractal Hausdorff and pre-packing dimensions.We also provide a relationship between the mutual multifractal Renyi dimensions of...In this paper,we compare the mutual multifractal Renyi dimensions to the´mutual multifractal Hausdorff and pre-packing dimensions.We also provide a relationship between the mutual multifractal Renyi dimensions of orthogonal projections´of a couple of measures(µ,ν)in R^(n).As an application,we study the mutual multifractal analysis of the projections of measures.展开更多
基金Supported in part by the NSF(A200913)of Heilongjiang Provincethe Scientific Tech-nical Research Project(12531720)of the Education Department of Heilongjiang Province+1 种基金Pre-Research Project(SY201224)of Provincial Key Innovationthe NSF(11161042)of China
文摘In this paper, the authors establish the boundedness of multilinear commutators generated by a Marcinkiewicz integral operator and a RBMO（μ） function on homogeneous Morrey-Herz spaces with non doubling measures.
基金supported by NSFC(11101447),supported by NSFC(11201500)
文摘We study the doubling property of binomial measures on generalized ternary Cantor subsets of [0, 1]. We find some new phenomena. There are three different cases. In the first case, we obtain an equivalent condition for the measure to be doubling. In the other cases, we show that the condition is not necessary. Then facts and partial results are discussed.
基金This work was supported by the National Natural Science Foundation of China （Grant Nos. 11171027, 11101339） and the Specialized Research Fund for the Doctoral Program of Higher Education of China （Grant No. 20120003110003）.
文摘Let μ be a nonnegative Radon measure on Rd which satisfies the polynomial growth condition that there exist positive constants Co and n ∈ （0,d） such that, for all x ∈ Rd and r 〉 0, μ（B（x, r））≤ Corn, where B（x, r） denotes the open ball centered at x and having radius r. In this paper, we show that, if μ（Rd） 〈∞, then the boundedness of a Calderdn-Zygmund operator T on L2（μ） is equivalent to that of T from the localized atomic Hardy space h1（μ） to L1,∞（μ） or from h1（μ） to L1（μ）.
文摘The mulfifractal formalism for single measure is reviewed. Next, a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Hausdorff and packing measures to a vector of simultaneously many measures. Borel-Cantelli and Large deviations Theorems are extended to higher orders and thus applied for the validity of the new variant of the multifractal formalism for some special cases of multi-doubling type measures.
基金financially supported by the ANR Micromorfing Program(ANR-14-CE07-0035)China Scholarship Council(CSC)the Labex Action
文摘Electronic speckle pattern interferometry（ESPI） and digital speckle pattern interferometry are wellestablished non-contact measurement methods. They have been widely used to carry out precise deformation mapping. However, the simultaneous two-dimensional（2D） or three-dimensional（3D） deformation measurements using ESPI with phase shifting usually involve complicated and slow equipment. In this Letter, we solve these issues by proposing a modified ESPI system based on double phase modulations with only one laser and one camera. In-plane normal and shear strains are obtained with good quality. This system can also be developed to measure 3D deformation, and it has the potential to carry out faster measurements with a highspeed camera.
文摘We survey some recent progress in the study of stability of elliptic Harnack inequalities under form-bounded perturbations for strongly local Dirichlet forms on complete locally compact separable metric spaces.
基金The first author is supported partly by the U.S. National Science Foundation Grant Nos. DMS96-22996 and DMS99-70352.supported partly by DGICYT Grant PB940192. Spainsupported partly by NATO Collaborative Research G
文摘Civen two doubling measures μ and v in a metric apace (S.p)of homogeneous type. let B_0 S be a given ball. It has been a well-known result bv now (see)[1 4])theat the validity of an L^1→L^1 Poincaré inequality of the following form: f_B|f-f_B|dv≤cr(B)f_Bgdμ. for all metric balls B B_0 S, implies a variant of representation formula of fractonal integral type: |f(x)-f_(B(11))|≤C integral from n=B_(11) g(y)p(x, y)/μ(B(x, p(x, y)))dμ(y)+C(r(B_0))/(μ(B_0))integral from n=B_0 g(y)dμ(y). One of the main results of this paper shows that an L^1 to L^q Poincaré inequality for some 01, i.e.. (f_B|f-f_B|~q dv)^(1/q)≤cr(B) f_B gdμ, for all metric balls B B_0. will suffice to imply the above representation formula. As an immediate corollary, we can show that the weak-type condition. sup_(λ>0)(λv({x ∈ B:|f(x)-f_B|>λ}))/v(B)≤Gr (B)f_B gdμ. also implies the same formula. Analogous theorems related to high-order Poincaréinequalities and Sobolev spaces in metric spaces are also proved.
文摘In this paper,we compare the mutual multifractal Renyi dimensions to the´mutual multifractal Hausdorff and pre-packing dimensions.We also provide a relationship between the mutual multifractal Renyi dimensions of orthogonal projections´of a couple of measures(µ,ν)in R^(n).As an application,we study the mutual multifractal analysis of the projections of measures.
