  The oxygen-isotope (^{16}O/^{18}O) effect (OIE) on the in-plane magnetic
penetration depth \lambda_{ab}(0) in optimally-doped YBa_2Cu_3O_{7-\delta} and
La_{1.85}Sr_{0.15}CuO_4, and in slightly underdoped YBa_2Cu_4O_8 and
Y_{0.8}Pr_{0.2}Ba_2Cu_3O_{7-\delta} was studied by means of muon-spin rotation.
A substantial OIE on \lambda_{ab}(0) with an OIE exponent
\beta_O=-d\ln\lambda_{ab}(0)/d\ln M_O\approx - 0.2 (M_O is the mass of the
oxygen isotope), and a small OIE on the transition temperature T_c with an OIE
exponent \alpha_O=-d\ln T_{c}/d \ln M_O\simeq0.02 to 0.1 were observed. The
observation of a substantial isotope effect on \lambda_{ab}(0), even in
cuprates where the OIE on T_c is small, indicates that lattice effects play an
important role in cuprate HTS.
