Weighted norm inequalities for fractional oscillatory integrals and applications

Abstract

We set up some weighted norm inequalities for fractional oscillatory integral operators. As applications, the corresponding results for commutators formed by BM O(R n ) functions and the operators are established.

Boundedness of oscillatory integral operators and their commutators on weighted Morrey spaces

“…The corresponding fractional oscillatory integral operator is defined by .14) where P (x, y) is also a real valued polynomial defined on R n × R n . Obviously, when α = 0, S 0 = S and K 0 = K. Recently, the authors of this paper obtained the weighted boundedness of S α in [20]. Partly motivated by the idea from [7] and the results of [11] as well as [20], we now give another two results of this paper…”

“…Obviously, when α = 0, S 0 = S and K 0 = K. Recently, the authors of this paper obtained the weighted boundedness of S α in [20]. Partly motivated by the idea from [7] and the results of [11] as well as [20], we now give another two results of this paper…”

“…Lemma 2.4. [20], [7] Let w ∈ A (p,q) , 0 < α < n, 1 < p < n α and 1 p − 1 q = α n . Then there exists constant C > 0 independent of P such that such that…”