Inclusion mappings between lp spaces

It is shown that the inclusion mapping from $\text{l}{}^{\mathrm{p}}\text{into}\text{l}{}^{\mathrm{q}}\text{is}\text{(}\text{2pq}\text{(pq ? 2p + 2q)}\text{, 1)}$-absolutely summing if 1 ? p ? q ? 2 and (p, 1)-absolutely summing if 1 ? p ? 2 ? q ? ∞ or 2 ? p ? q ? ∞. As a corollary, it follows that a (p, 1)-absolutely summing operator, p > 1, need not have the Dunford-Pettis property; this observation answering a question raised by Pelczynski.