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Global orthogonality implies local almost-orthogonality.

J. Michael Wilson — 2000

Revista Matemática Iberoamericana

We introduce a new stopping-time argument, adapted to handle linear sums of noncompactly-supported functions that satisfy fairly weak decay, smoothness, and cancellation conditions. We use the argument to obtain a new Littlewood-Paley-type result for such sums.

Weighted two-parameter Bergman space inequalities.

J. Michael Wilson — 2003

Publicacions Matemàtiques

Weighted inequalities for gradients on non-smooth domains

Caroline Sweezy; J. Michael Wilson — 2010

We prove sufficiency of conditions on pairs of measures μ and ν, defined respectively on the interior and the boundary of a bounded Lipschitz domain Ω in d-dimensional Euclidean space, which ensure that, if u is the solution of the Dirichlet problem. Δu = 0 in Ω, ${u |}_{\partial Ω} = f$ , with f belonging to a reasonable test class, then $(\int_{Ω} {| \nabla u |}^{q} {d μ)}^{1 / q} \leq (\int_{\partial Ω} {| f |}^{p} {d ν)}^{1 / p}$ , where 1 < p ≤ q < ∞ and q ≥ 2. Our sufficiency conditions resemble those found by Wheeden and Wilson for the Dirichlet problem on $ℝ ₊^{d + 1}$ . As in that case we attack the problem by...

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Currently displaying 1 – 6 of 6

Global orthogonality implies local almost-orthogonality.

Weighted two-parameter Bergman space inequalities.

Weighted inequalities for gradients on non-smooth domains

Weighted L... Estimates for Derivates of Weighted H... Functions.

A mathematical model of a micrometastasis.

The non-uniform spatial development of a micrometastasis.