Weighted norm inequalities for oscillatory integrals with finite type phases on the line

作者：Bennett Jonathan^*; Harrison Samuel

来源：Advances in Mathematics, 2012, 229(4): 2159-2183.

DOI：10.1016/j.aim.2011.12.014

• Weighted inequalities
• Oscillatory integrals
• Convolution

We obtain two-weighted L-2 norm inequalities for oscillatory integral operators of convolution type on the line whose phases are of finite type. The conditions imposed on the weights involve geometrically-defined maximal functions, and the inequalities are best-possible in the sense that they imply the full L-p (R) -%26gt; L-q (R) mapping properties of the oscillatory integrals. Our results build on work of Carbery, Soria, Vargas and the first author.

• 出版日期2012-3-1