On the bilinear square Fourier multiplier operators and related multilinear square functions
Zengyan Si, Qingying Xue, Kozo Yabuta

TL;DR
This paper establishes boundedness results for bilinear square Fourier multiplier operators and related multilinear square functions in weighted Lebesgue spaces, including endpoint and commutator estimates, by analyzing kernel regularity and improving key lemmas.
Contribution
It provides new boundedness criteria for bilinear square Fourier multipliers and multilinear square functions, extending previous results with refined techniques and endpoint estimates.
Findings
Boundedness of rak{T}_m in weighted L^p spaces for certain p ranges.
Weak-type endpoint estimates involving L log L spaces.
Boundedness of commutators of rak{T}_m with weighted estimates.
Abstract
Let and be the bilinear square Fourier multiplier operator associated with a symbol , which is defined by Let be an integer with and be a number satisfying . Suppose that and each is a nonnegative function on . In this paper, we show that is bounded from to if with . Moreover, if and or , then is bounded from $L^{p_1}(\omega_1)\times…
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Advanced Mathematical Physics Problems · Mathematical Analysis and Transform Methods
