Generic Multilinear Multipliers Associated to Degenerate Simplexes
Robert M. Kesler

TL;DR
This paper proves boundedness of a class of degenerate multilinear multipliers associated with simplexes, extending their action to certain Lebesgue and Wiener spaces under specific conditions.
Contribution
It establishes the boundedness of generic degenerate trilinear simplex multipliers on mixed Lebesgue and Wiener spaces, generalizing previous results to degenerate cases.
Findings
Boundedness of the multiplier on specified function spaces.
Extension to Wiener spaces $W_p(R)$ under Hörmander-Mikhlin conditions.
Applicable for a range of $p_1, p_2, p_3$ satisfying given inequalities.
Abstract
For each , let with norm . Moreover, let and satisfy the H\"{o}rmander-Mikhlin condition \begin{eqnarray*} \left| \partial^{\vec{\alpha}} a_j \left(\vec{\xi}\right) \right| \lesssim_{\vec{\alpha}} \frac{1}{dist(\vec{\xi}, \Gamma)^{|\vec{\alpha}|}}~~~\forall \vec{\xi} \in \mathbb{R}^2, j \in \{1, 2\} \end{eqnarray*} for sufficiently many multi-indices . Our main result is that the generic degenerate trilinear simplex multiplier defined on by \begin{eqnarray*} B[a_1, a_2] : (f_1, f_2, f_3) \rightarrow…
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Nonlinear Partial Differential Equations · Advanced Mathematical Physics Problems
