Displaying similar documents to “A system of partial differential equations with fractional derivatives.”

Second order unbounded parabolic equations in separated form

Maciej Kocan, Andrzej Święch (1995)

Studia Mathematica

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We prove existence and uniqueness of viscosity solutions of Cauchy problems for fully nonlinear unbounded second order Hamilton-Jacobi-Bellman-Isaacs equations defined on the product of two infinite-dimensional Hilbert spaces H'× H'', where H'' is separable. The equations have a special "separated" form in the sense that the terms involving second derivatives are everywhere defined, continuous and depend only on derivatives with respect to x'' ∈ H'', while the unbounded terms are of...

Some integral and maximal operators related to starlike sets

Sagun Chanillo, David Watson, Richard Wheeden (1993)

Studia Mathematica

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We prove two-weight norm estimates for fractional integrals and fractional maximal functions associated with starlike sets in Euclidean space. This is seen to include general positive homogeneous fractional integrals and fractional integrals on product spaces. We consider both weak type and strong type results, and we show that the conditions imposed on the weight functions are fairly sharp.

Equiconvergence for Laguerre function series

Krzysztof Stempak (1996)

Studia Mathematica

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We prove an equiconvergence theorem for Laguerre expansions with partial sums related to partial sums of the (non-modified) Hankel transform. Combined with an equiconvergence theorem recently proved by Colzani, Crespi, Travaglini and Vignati this gives, via the Carleson-Hunt theorem, a.e. convergence results for partial sums of Laguerre function expansions.