Rocha, Pablo; Urciuolo, Marta On the \(H^p\)-\(L^p\)-boundedness of some integral operators. (English) Zbl 1230.42030 Georgian Math. J. 18, No. 4, 801-808 (2011). Summary: We obtain the \(H^p(\mathbb{R}^n)\to L^p(\mathbb{R}^n)\) boundedness, \(0<p\leq 1\), of integral operators of the form \[ Tf(x)=\int |x-a_1y|^{-\alpha_1}\cdots |x-a_my|^{-\alpha_m}f(y)dy, \]\(\alpha_1+\dots \alpha_m=n\) and \(a_i\{0\}\), \(a_i\neq a_j\) for \(i\neq j\), \(1\leq i, j\leq m\). We also show that these operators are not bounded on \(H^p(\mathbb{R})\). Cited in 6 Documents MSC: 42B30 \(H^p\)-spaces 42B25 Maximal functions, Littlewood-Paley theory 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.) Keywords:integral operators; Hardy spaces PDFBibTeX XMLCite \textit{P. Rocha} and \textit{M. Urciuolo}, Georgian Math. J. 18, No. 4, 801--808 (2011; Zbl 1230.42030) Full Text: DOI References: [1] Godoy T., Rev. Un. Mat. Argentina 38 pp 3– (1993) [2] DOI: 10.1023/A:1026437621978 · Zbl 0937.47032 · doi:10.1023/A:1026437621978 [3] Mikhailov L. G., Dokl. Akad. Nauk SSSR 176 pp 263– (1967) [4] DOI: 10.1007/BF01161645 · Zbl 0638.42019 · doi:10.1007/BF01161645 [5] DOI: 10.1007/s10587-005-0032-y · Zbl 1081.42018 · doi:10.1007/s10587-005-0032-y This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.