JournalszaaVol. 21, No. 4pp. 915–929

LpLqL_p-L_q Estimates for the Bochner-Riesz Operator of Complex Order

  • Denis N. Karasev

    Rostov University, Rostov-on-Don, Russian Federation
  • V.A. Nogin

    Rostov University, Rostov-on-Don, Russian Federation
$L_p-L_q$ Estimates for the Bochner-Riesz Operator of Complex Order cover
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Abstract

We describe convex sets on the (1p,1q(\frac{1}{p}, \frac{1}{q})-plane for which the well-known Bochner-Riesz operator with the symbol (1ξ2)+α(0<Reα<n+12)(1–|\xi|^2)+^{–\alpha} (0 < \mathrm {Re} \alpha < \frac{n+1}{2}) is bounded from LpL_p into LqL_q.

Cite this article

Denis N. Karasev, V.A. Nogin, LpLqL_p-L_q Estimates for the Bochner-Riesz Operator of Complex Order. Z. Anal. Anwend. 21 (2002), no. 4, pp. 915–929

DOI 10.4171/ZAA/1117