Geodesic
Estimates for oscillatory singular integrals on Hardy spaces
Hussain Al-Qassem 1   ; Leslie Cheng 2   ; Yibiao Pan 3
1 Department of Mathematics and Physics Qatar University Doha, Qatar
2 Department of Mathematics Bryn Mawr College Bryn Mawr, PA 19010, U.S.A.
3 Department of Mathematics University of Pittsburgh Pittsburgh, PA 15260, U.S.A.
Studia Mathematica, Tome 224 (2014) no. 3, pp. 277-289 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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For any $n \in \mathbb {N}$, we obtain a bound for oscillatory singular integral operators with polynomial phases on the Hardy space $H^1(\mathbb {R}^n)$. Our estimate, expressed in terms of the coefficients of the phase polynomial, establishes the $H^1$ boundedness of such operators in all dimensions when the degree of the phase polynomial is greater than one. It also subsumes a uniform boundedness result of Hu and Pan (1992) for phase polynomials which do not contain any linear terms. Furthermore, the bound is shown to be valid on weighted Hardy spaces as well if the weights belong to the Muckenhoupt class $A_1$.
DOI : 10.4064/sm224-3-5
Keywords: mathbb obtain bound oscillatory singular integral operators polynomial phases hardy space mathbb estimate expressed terms coefficients phase polynomial establishes boundedness operators dimensions degree phase polynomial greater subsumes uniform boundedness result pan phase polynomials which contain linear terms furthermore bound shown valid weighted hardy spaces weights belong muckenhoupt class nbsp

Hussain Al-Qassem  1   ; Leslie Cheng  2   ; Yibiao Pan  3

1 Department of Mathematics and Physics Qatar University Doha, Qatar
2 Department of Mathematics Bryn Mawr College Bryn Mawr, PA 19010, U.S.A.
3 Department of Mathematics University of Pittsburgh Pittsburgh, PA 15260, U.S.A. 
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Hussain Al-Qassem; Leslie Cheng; Yibiao Pan. Estimates for oscillatory singular integrals on Hardy spaces. Studia Mathematica, Tome 224 (2014) no. 3, pp. 277-289. doi: 10.4064/sm224-3-5

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