查看更多>>摘要：This paper is a summary of the research on the mapping properties of sin-gular integrals with rough kernels and the corresponding maximal operators.More precisely,the author presents some recent progress,interesting problems and typi-cal methods used in the theory concerning the boundedness and continuity for the rough singular integral operators and maximal singular integral operators along cer-tain submanifolds such as polynomial mappings,polynomial curves,homogeneous mappings,surfaces of revolution and real-analytic submanifolds on the Lebesgue spaces,Triebel-Lizorkin spaces,Besov spaces and mixed radial-angular spaces.
查看更多>>摘要：The main aim of this paper is to derive some new summation theorems for terminating and truncated Clausen's hypergeometric series with unit argument,when one numerator parameter and one denominator parameter are negative integers.Further,using our truncated summation theorems,we obtain the Mellin transforms of the product of exponential function and Goursat's truncated hypergeometric function.
查看更多>>摘要：In this paper,we derive the interior gradient estimate for solutions to gen-eral prescribed curvature equations.The proof is based on a fundamental observation of Gårding's cone and some delicate inequalities under a suitably chosen coordinate chart.As an application,we obtain a Liouville type theorem.
查看更多>>摘要：In this note we show that the general theory of vector valued singular inte-gral operators of Calderón-Zygthmund defined on general metric measure spaces,can be applied to obtain Sobolev type regularity properties for solutions of the dyadic frac-tional Laplacian.In doing so,we define parhal derivatives in terms of Haar multipliers and dyadic homogeneous singular integral operators.
查看更多>>摘要：The article considers the controllability of a diffusion equation with frac-tional integro-differential expressions.We prove that the resulting equation is null-controllable in arbitrary small time.Our method reduces essentially to the study of classical moment problems.
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