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71.
In this paper, the authors establish several general theorems for the boundedness of sublinear operators (B sublinear operators) satisfies the condition (1.2), generated by B singular integrals on a weighted Lebesgue spaces $L_{p,\omega,\gamma}(\mathbb{R}_{k,+}^{n})$ , where $B=\sum_{i=1}^{k} (\frac{\partial^{2}}{\partial x_{k}^{2}} + \frac{\gamma_{i}}{x_{i}}\frac{\partial}{\partial x_{i}} )$ . The condition (1.2) are satisfied by many important operators in analysis, including B maximal operator and B singular integral operators. Sufficient conditions on weighted functions ω and ω 1 are given so that B sublinear operators satisfies the condition (1.2) are bounded from $L_{p,\omega,\gamma}(\mathbb{R}_{k,+}^{n})$ to $L_{p,\omega_{1},\gamma}(\mathbb{R}_{k,+}^{n})$ . 相似文献
72.
Expanded bodipy dyes: anion sensing using a bodipy analog with an additional difluoroboron bridge 总被引:1,自引:0,他引:1
Oxalyl-tethered pyrroles can be doubly bridged with two difluoroboron chelating units to yield bright orange dyes. Interestingly, in polar organic solvents, the addition of fluoride and cyanide result in reversible detachment of the otherwise stable difluoroboron bridges, resulting in sharp changes in color. Thus, this novel compound behaves as a highly selective chromogenic sensor for fluoride and cyanide ions. 相似文献
73.
We consider the generalized shift operator associated with the Laplace-Bessel differential operator $$ \Delta _B = \sum\limits_{i = 1}^n {\frac{{\partial ^2 }} {{\partial x_j^2 }}} + \sum\limits_{i = 1}^k {\frac{{\gamma _i }} {{x_i }}\frac{\partial } {{\partial x_i }}} $$ , and study the modified B-Riesz potential ? α, β generated by the generalized shift operator acting in the B-Morrey space in the limiting case. We prove that the operator ? α, β, 0 < α < n + |γ|, is bounded from the B-Morrey space L (n+|γ|?λ)/α,λ,γ (? k,+ n ) to the B-BMO space BMO γ (? k,+ n ). 相似文献