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Search: All articles in the CMB digital archive with keyword norm estimates

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1. CMB 2011 (vol 55 pp. 689)

Berndt, Ryan
A Pointwise Estimate for the Fourier Transform and Maxima of a Function
We show a pointwise estimate for the Fourier transform on the line involving the number of times the function changes monotonicity. The contrapositive of the theorem may be used to find a lower bound to the number of local maxima of a function. We also show two applications of the theorem. The first is the two weight problem for the Fourier transform, and the second is estimating the number of roots of the derivative of a function.

Keywords:Fourier transform, maxima, two weight problem, roots, norm estimates, Dirichlet-Jordan theorem
Categories:42A38, 65T99

2. CMB 2000 (vol 43 pp. 406)

Borwein, David
Weighted Mean Operators on $l_p$
The weighted mean matrix $M_a$ is the triangular matrix $\{a_k/A_n\}$, where $a_n > 0$ and $A_n := a_1 + a_2 + \cdots + a_n$. It is proved that, subject to $n^c a_n$ being eventually monotonic for each constant $c$ and to the existence of $\alpha := \lim \frac{A_n}{na_n}$, $M_a \in B(l_p)$ for $1 < p < \infty$ if and only if $\alpha < p$.

Keywords:weighted means, operators on $l_p$, norm estimates
Categories:47B37, 47A30, 40G05

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