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51. CMB 1998 (vol 41 pp. 404)
$L^p$boundedness of a singular integral operator Let $b(t)$ be an $L^\infty$ function on $\bR$, $\Omega (\,y')$ be
an $H^1$ function on the unit sphere satisfying the mean zero
property (1) and $Q_m(t)$ be a real polynomial on $\bR$ of degree
$m$ satisfying $Q_m(0)=0$. We prove that the singular integral
operator
$$
T_{Q_m,b} (\,f) (x)=p.v. \int_\bR^n b(y) \Omega(\,y) y^{n} f
\left( xQ_m (y) y' \right) \,dy
$$
is bounded in $L^p (\bR^n)$ for $1

52. CMB 1998 (vol 41 pp. 306)
Oscillatory integrals with nonhomogeneous phase functions related to SchrÃ¶dinger equations In this paper we consider solutions to the free Schr\" odinger
equation in $n+1$ dimensions. When we restrict the last variable
to be a smooth function of the first $n$ variables we find that the
solution, so restricted, is locally in $L^2$, when the initial data
is in an appropriate Sobolev space.
Categories:42A25, 42B25 
53. CMB 1998 (vol 41 pp. 49)
Stability of weighted darma filters We study the stability of linear filters associated with certain types of
linear difference equations with variable coefficients. We show that
stability is determined by the locations of the poles of a rational transfer
function relative to the spectrum of an associated weighted shift operator.
The known theory for filters associated with constantcoefficient difference
equations is a special case.
Keywords:Difference equations, adaptive $\DARMA$ filters, weighted shifts,, stability and boundedness, automatic continuity Categories:47A62, 47B37, 93D25, 42A85, 47N70 
54. CMB 1997 (vol 40 pp. 433)
A uniform $L^{\infty}$ estimate of the smoothing operators related to plane curves In dealing with the spectral synthesis property for a plane curve with
nonzero curvature, a key step is to have a uniform $L^{\infty}$ estimate
for some smoothing operators related to the curve. In this paper, we will
show that the same $L^{\infty}$ estimate holds true for a plane curve
that may have zero curvature.
Categories:42b20, 42b15 
55. CMB 1997 (vol 40 pp. 296)
A general approach to LittlewoodPaley theorems for orthogonal families A general lacunary LittlewoodPaley type theorem is proved, which applies in a
variety of settings including Jacobi polynomials in $[0, 1]$, $\su$, and the
usual classical trigonometric series in $[0, 2 \pi)$. The theorem is used to
derive new results for $\LP$ multipliers on $\su$ and Jacobi $\LP$ multipliers.
Categories:42B25, 42C10, 43A80 
56. CMB 1997 (vol 40 pp. 169)
The class $A^{+}_{\infty}(\lowercase{g})$ and the onesided reverse HÃ¶lder inequality We give a direct proof that $w$ is an $A^{+}_{\infty}(g)$ weight if and only
if $w$ satisfies a onesided, weighted reverse H\"older inequality.
Keywords:onesided maximal operator, onesided $(A_\infty)$, onesided, reverse HÃ¶lder inequality Category:42B25 