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【期刊论文】Spectral Theory of Riesz Potentials on Quasi–Metric Spaces
杨大春, Hans Triebel, Dachun Yang
Math. Nachr. 238(2002), 160-184,-0001,():
-1年11月30日
This paper deals with spectral assertions of Riesz potentials in some classes of quasimetric spaces. In addition we survey briefly a few related subjects: integral operators, local means and function spaces, euclidean charts of quasi–metric spaces, relations to fractal geometry.
Riesz potentials, eigenvalue distributions, spaces of homogeneous type, Besov spaces, entropy numbers
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【期刊论文】BOUNDEDNESS OF SINGULAR INTEGRALS OF VARIABLE ROUGH CALDERON-ZYGMUND KERNELS ALONG SURFACES
杨大春, LIN TANG, DACHUN YANG
Integr. Equ. oper. Theory 43(2002)488-502,-0001,():
-1年11月30日
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【期刊论文】Riesz Potentials in Besov and Triebel–Lizorkin Spaces over Spaces of Homogeneous Type
杨大春, DACHUN YANG
Potential Analysis 19: 193-210, 2003,-0001,():
-1年11月30日
By using the discrete Calderón reproducing formulae, the author first establishes the boundedness of the Riesz-potential-type operator in homogeneous Besov and Triebel–Lizorkin spaces over spaces of homogeneous type. Then, by use of the T 1 theorems for these spaces, the author proves that this operator of Riesz potential type can be used as the lifting operator of these spaces.
space of homogeneous type, Riesz potential, Besov space, Triebel–Lizorkin space
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【期刊论文】Besov spaces on spaces of homogeneous type and fractals
杨大春, Dachun Yang
STUDIA MATHEMATICA 156(1)(2003),-0001,():
-1年11月30日
Let Γ be a compact d-set in Rn with 0 < d ≤n, which includes various kinds of fractals. The author shows that the Besov spaces Bspq(Γ) defined by two different and equivalent methods, namely, via traces and quarkonial decompositions in the sense of Triebel are the same spaces as those obtained by regarding Γ as a space of homogeneous type when 0 < s < 1, 1 < p <∞ and 1≤q≤∞.
Besov spaces, atoms, blocks, d-sets, fractals, spaces of homogeneous type
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【期刊论文】Some new spaces of Besov and Triebel-Lizorkin type on homogeneous spaces
杨大春, Yongsheng Han, Dachun Yang
STUDIA MATHEMATICA 156(1)(2003),-0001,():
-1年11月30日
New norms for some distributions on spaces of homogeneous type which include some fractals are introduced. Using inhomogeneous discrete Calderon reproducing formulae and the Plancherel-Polya inequalities on spaces of homogeneous type, the authors prove that these norms give a new characterization for the Besov and Triebel-Lizorkin spaces with p; q > 1 and can be used to introduce new inhomogeneous Besov and Triebel-Lizorkin spaces with p; q≤ 1 on spaces of homogeneous type. Moreover, atomic decompositions of these new spaces are also obtained. All the results of this paper are new even for Rn.
space of homogeneous type, Plancherel-Polya inequality, Besov space, Triebel-Lizorkin space, Calderon reproducing formula, Littlewood-Paley Sfunction, Littlewood-Paley g-function, unit, molecule
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