scholarly journals Logarithmic Bounds for Oscillatory Singular Integrals on Hardy Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Hussain Al-Qassem ◽  
Leslie Cheng ◽  
Yibiao Pan
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Singular Integrals ◽  
Rate Of Growth ◽  
Oscillatory Singular Integrals

We establish a logarithmic bound for oscillatory singular integrals with quadratic phases on the Hardy spaceH1(Rn). The logarithmic rate of growth is the best possible.

Oscillatory singular integral operators with Hölder class kernels on Hardy spaces

2019 ◽  
Vol 31 (2) ◽  
pp. 535-542
Author(s):  
Yibiao Pan
Keyword(s):  
Singular Integral ◽  
Hardy Spaces ◽  
Singular Integrals ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Oscillatory Singular Integral ◽  
Hölder Class ◽  
Holder Class ◽  
Oscillatory Singular Integrals

AbstractA sharp logarithmic bound is established for the {H^{1}}-norm of oscillatory singular integrals with quadratic phases and Hölder class kernels. Prior results had relied on a {C^{1}}-assumption on the kernel.

Sharp bounds for oscillatory singular integrals on Hardy spaces

2017 ◽  
Vol 238 (2) ◽  
pp. 121-132
Author(s):  
Hussain Al-Qassem ◽  
Leslie Cheng ◽  
Yibiao Pan
Keyword(s):  
Hardy Spaces ◽  
Singular Integrals ◽  
Sharp Bounds ◽  
Oscillatory Singular Integrals

H1 boundedness of oscillatory singular integrals with degenerate phase functions

1994 ◽  
Vol 116 (2) ◽  
pp. 353-358
Author(s):  
Yibiao Pan
Keyword(s):  
Hardy Space ◽  
Singular Integral ◽  
Phase Function ◽  
Infinite Order ◽  
Singular Integrals ◽  
Integral Operators ◽  
Uniform Boundedness ◽  
Sufficient Condition ◽  
Oscillatory Singular Integrals ◽  
Phase Functions

AbstractIn this paper we study the uniform boundedness of oscillatory singular integral operators with degenerate phase functions on the Hardy space H1. The H1 boundedness was previously known when the phase function is nondegenerate. Here we obtain a sufficient condition for H1 boundedness which allows the phase function vanishing to infinite order.

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