Bilinear multipliers on Lorenzt spaces
Francisco Villarroya
TL;DR
This paper investigates conditions for the boundedness of bilinear multiplier operators related to the bilinear Hilbert transform on Lebesgue and Lorentz spaces, providing new theoretical insights.
Contribution
It offers one sufficient and two necessary conditions for the boundedness of these bilinear operators, advancing understanding of their behavior on Lorentz spaces.
Findings
Established a sufficient condition for boundedness.
Identified two necessary conditions for boundedness.
Connected results to the bilinear Hilbert transform.
Abstract
We give one sufficient and two necessary conditions for boundedness between Lebesgue or Lorentz spaces of several classes of bilinear multiplier operators closely connected with the bilinear Hilbert transform.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Advanced Harmonic Analysis Research · Advanced Mathematical Physics Problems