  We study kernel least-squares estimation under a norm constraint. This form
of regularisation is known as Ivanov regularisation and it provides better
control of the norm of the estimator than the well-established Tikhonov
regularisation. Ivanov regularisation can be studied under minimal assumptions.
In particular, we assume only that the RKHS is separable with a bounded and
measurable kernel. We provide rates of convergence for the expected squared
$L^2$ error of our estimator under the weak assumption that the variance of the
response variables is bounded and the unknown regression function lies in an
interpolation space between $L^2$ and the RKHS. We then obtain faster rates of
convergence when the regression function is bounded by clipping the estimator.
In fact, we attain the optimal rate of convergence. Furthermore, we provide a
high-probability bound under the stronger assumption that the response
variables have subgaussian errors and that the regression function lies in an
interpolation space between $L^\infty$ and the RKHS. Finally, we derive
adaptive results for the settings in which the regression function is bounded.
