Rough Marcinkiewicz integrals on product spaces [PDF]
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Rough Marcinkiewicz integral operators on product spaces
Let \(d\geq 2\) (\(d= n\) or \(d=m\)) and \(S^{d-1}\) be the unit sphere in \(\mathbb{R}^d\) equipped with the normalized Lebesgue measure \(d\sigma\). Suppose that \(\Omega(x,y)\) is a homogeneous function of degree zero in both variables \(x\) and \(y\) and it satisfies \(\Omega\in L(S^{n-1}\times S^{m-1})\) and \[ \int_{S^{n-1}} \Omega(x,y)\,d\sigma(
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