Homogeneous fractional integrals on Hardy spaces
Copyright policy )Homogeneous fractional integrals on Hardy spaces
Let \(S^{n-1}\) be the unit sphere in the \(n\) dimensional Euclidean space \(\mathbb R^n\). Suppose \(0n/(n-\alpha)\). Suppose \(\int_{0}^{1}\omega_r(\delta)\delta^{-1-\alpha} d \delta0\) such that \(\|T_{\Omega, \alpha}f\|_{L^q}\leq C\|f\|_{H^p}\). Here, \(\omega_r(\delta)=\sup_{|\rho-I|<\delta}\left(\int_{S^{n-1}} |\Omega(\rho x')-\Omega(x')|^r dx'\right)^{1/r}\), \(\rho\) is a rotation in \(\mathbb R^n\) and \(I\) is the identity operator. Results for \((H^1, L^{n/(n-\alpha)})\) and \((H^p, H^q)\) are also given.
- Beijing Normal University China (People's Republic of)
- Beijing Normal University China (People's Republic of)
fractional integral, $H^p$ space, Singular and oscillatory integrals (Calderón-Zygmund, etc.), Maximal functions, Littlewood-Paley theory, Hardy space, \(H^p\)-spaces, $L^r$-Dini condition, Dini condition, \(H^p\) space, 42B25, homogeneous kernel, Fractional integral
fractional integral, $H^p$ space, Singular and oscillatory integrals (Calderón-Zygmund, etc.), Maximal functions, Littlewood-Paley theory, Hardy space, \(H^p\)-spaces, $L^r$-Dini condition, Dini condition, \(H^p\) space, 42B25, homogeneous kernel, Fractional integral
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