Abstract
Oscillatory integral operators play a key role in harmonic analysis. In this paper, the authors investigate the boundedness of the oscillatory singular integrals with variable Calderón-Zygmund kernel on the weighted Morrey spacesLp,k(ω). Meanwhile, the corresponding results for the oscillatory singular integrals with standard Calderón-Zygmund kernel are established.
Highlights
Introduction and Main ResultsSuppose that k is the standard Calderon-Zygmund kernel.That is, k ∈ C∞(Rn \ {0}) is homogeneous of degree n, and∫inΣtkeg(xra)dl oσpxe=ra0to, rwThλeriesΣ = {x ∈ Rn defined by : |x| = 1}
In 2009, Komori and Shirai [4] first defined the weighted Morrey spaces Lp,κ(ω) which could be viewed as an extension of weighted Lebesgue spaces
They studied the boundedness of the fractional integral operator, the Hardy-Littlewood maximal operator, and the Calderon-Zygmund singular integral operator on the space
Summary
Suppose that k is the standard Calderon-Zygmund kernel. :. Define the oscillatory integral operator with variable Calderon-Zygmund kernel Tλ∗ by. In 2009, Komori and Shirai [4] first defined the weighted Morrey spaces Lp,κ(ω) which could be viewed as an extension of weighted Lebesgue spaces They studied the boundedness of the fractional integral operator, the Hardy-Littlewood maximal operator, and the Calderon-Zygmund singular integral operator on the space. Shi et al [18] obtained the boundedness of a class of oscillatory integrals with Calderon-Zygmund kernel and polynomial phase on weighted Morrey spaces. For any 1 < p < ∞, 0 < κ < 1, and ω ∈ Ap, Tλ∗ is bounded on Lp,κ(ω)
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