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Zeitschrift für Analysis und ihre Anwendungen


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Volume 21, Issue 4, 2002, pp. 915–929
DOI: 10.4171/ZAA/1117

Published online: 2002-12-31

$L_p-L_q$ Estimates for the Bochner-Riesz Operator of Complex Order

Denis N. Karasev[1] and V.A. Nogin[2]

(1) Rostov University, Rostov-on-Don, Russian Federation
(2) Rostov University, Rostov-on-Don, Russian Federation

We describe convex sets on the $(\frac{1}{p}, \frac{1}{q}$)-plane for which the well-known Bochner-Riesz operator with the symbol $(1–|\xi|^2)+^{–\alpha} (0 < \mathrm {Re} \alpha < \frac{n+1}{2})$ is bounded from $L_p$ into $L_q$.

Keywords: Bochner-Riesz operator, potential-type operator, oscillating kernel, $L_p-L_q$ estimates

Karasev Denis, Nogin V.A.: $L_p-L_q$ Estimates for the Bochner-Riesz Operator of Complex Order. Z. Anal. Anwend. 21 (2002), 915-929. doi: 10.4171/ZAA/1117