1. CJM 2013 (vol 65 pp. 1217)
|Beltrami Equation with Coefficient in Sobolev and Besov Spaces|
Our goal in this work is to present some function spaces on the complex plane $\mathbb C$, $X(\mathbb C)$, for which the quasiregular solutions of the Beltrami equation, $\overline\partial f (z) = \mu(z) \partial f (z)$, have first derivatives locally in $X(\mathbb C)$, provided that the Beltrami coefficient $\mu$ belongs to $X(\mathbb C)$.
Keywords:quasiregular mappings, Beltrami equation, Sobolev spaces, CalderÃ³n-Zygmund operators
Categories:30C62, 35J99, 42B20
2. CJM 2000 (vol 52 pp. 381)
|Hardy Space Estimate for the Product of Singular Integrals |
$H^p$ estimate for the multilinear operators which are finite sums of pointwise products of singular integrals and fractional integrals is given. An application to Sobolev space and some examples are also given.
Keywords:$H^p$ space, multilinear operator, singular integral, fractional integration, Sobolev space
3. CJM 1997 (vol 49 pp. 74)
|Constrained approximation in Sobolev spaces |
Positive, copositive, onesided and intertwining (co-onesided) polynomial and spline approximations of functions $f\in\Wp^k\mll$ are considered. Both uniform and pointwise estimates, which are exact in some sense, are obtained.
Keywords:Constrained approximation, polynomials, splines, degree of, approximation, $L_p$ space, Sobolev space
Categories:41A10, 41A15, 41A25, 41A29