It is important to calculate the Hausdorff dimension and the Hausdorff mesure respect to this dimension for some fractal sets. By using the usual method of “Mass Distribution”, we can only calculate the Hausdorff di...It is important to calculate the Hausdorff dimension and the Hausdorff mesure respect to this dimension for some fractal sets. By using the usual method of “Mass Distribution”, we can only calculate the Hausdorff dimension. In this paper, we will construct an integral formula by using lower inverse s-density and then use it to calculate the Hausdorff measures for some fractional dimensional sets.展开更多
Let mu be a locally uniformly alpha-dimensional measure on R-n and P-t(fd mu) be the Able Poisson means of Hermite expansions for f is an element of L-p(d mu), it is studied that the asymptotis properties of P-t(fd mu...Let mu be a locally uniformly alpha-dimensional measure on R-n and P-t(fd mu) be the Able Poisson means of Hermite expansions for f is an element of L-p(d mu), it is studied that the asymptotis properties of P-t(fd mu) as t --> 1_. Analogue of Wiener's theorem is obtained. Author also establishs the boundedness of the alpha-dimensional maximal conjugate Poisson integral operators from L-p(d mu) to the Lebesgne p-power integrable function spaces L-p(dx), and this derives directly the boundedness of Riesz transforms.展开更多
Let M=ρ^(-1)I∈Mn(R)be an expanding matrix with 0<|ρ|<1 and D■Z^(n)be a finite digit set with O∈D and Z(mD)■Z(mD)■Z(mD)∪{0}■m^(-1)z^(n)for a prime m,where Z(mD):=(Ede emi(a)=O),LetμM.D be theassociateds...Let M=ρ^(-1)I∈Mn(R)be an expanding matrix with 0<|ρ|<1 and D■Z^(n)be a finite digit set with O∈D and Z(mD)■Z(mD)■Z(mD)∪{0}■m^(-1)z^(n)for a prime m,where Z(mD):=(Ede emi(a)=O),LetμM.D be theassociatedsel-simiar measure defined by M.DO)-ZaeDμM,D(M()-d).In this paper,the necessary and sufficient conditions for L2(μM,D)to admit infinite orthogonal exponential functions are given.Moreover,by using the order theory of polynomial,we estimate the number of orthogonal exponential functions for all cases that L^(2)(μM,D)does not admit infinite orthogonal exponential functions.展开更多
文摘It is important to calculate the Hausdorff dimension and the Hausdorff mesure respect to this dimension for some fractal sets. By using the usual method of “Mass Distribution”, we can only calculate the Hausdorff dimension. In this paper, we will construct an integral formula by using lower inverse s-density and then use it to calculate the Hausdorff measures for some fractional dimensional sets.
文摘Let mu be a locally uniformly alpha-dimensional measure on R-n and P-t(fd mu) be the Able Poisson means of Hermite expansions for f is an element of L-p(d mu), it is studied that the asymptotis properties of P-t(fd mu) as t --> 1_. Analogue of Wiener's theorem is obtained. Author also establishs the boundedness of the alpha-dimensional maximal conjugate Poisson integral operators from L-p(d mu) to the Lebesgne p-power integrable function spaces L-p(dx), and this derives directly the boundedness of Riesz transforms.
基金Supported by the NNSF of China(Grant Nos.12071125,12001183 and 11831007)the Hunan Provincial NSF(Grant Nos.2020JJ5097 and 2019JJ20012)the SRF of Hunan Provincial Education Department(Grant No.19B117)。
文摘Let M=ρ^(-1)I∈Mn(R)be an expanding matrix with 0<|ρ|<1 and D■Z^(n)be a finite digit set with O∈D and Z(mD)■Z(mD)■Z(mD)∪{0}■m^(-1)z^(n)for a prime m,where Z(mD):=(Ede emi(a)=O),LetμM.D be theassociatedsel-simiar measure defined by M.DO)-ZaeDμM,D(M()-d).In this paper,the necessary and sufficient conditions for L2(μM,D)to admit infinite orthogonal exponential functions are given.Moreover,by using the order theory of polynomial,we estimate the number of orthogonal exponential functions for all cases that L^(2)(μM,D)does not admit infinite orthogonal exponential functions.
