Estimates for oscillatory singular integrals on Hardy spaces
Studia Mathematica, Tome 224 (2014) no. 3, pp. 277-289
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $A_1$.
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
Affiliations des auteurs :
Hussain Al-Qassem 1 ; Leslie Cheng 2 ; Yibiao Pan 3
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author = {Hussain Al-Qassem and Leslie Cheng and Yibiao Pan},
title = {Estimates for oscillatory singular integrals on {Hardy} spaces},
journal = {Studia Mathematica},
pages = {277--289},
publisher = {mathdoc},
volume = {224},
number = {3},
year = {2014},
doi = {10.4064/sm224-3-5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm224-3-5/}
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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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