  In this study, we develop an asymptotic theory of nonparametric regression
for locally stationary random fields (LSRFs) $\{{\bf X}_{{\bf s}, A_{n}}: {\bf
s} \in R_{n} \}$ in $\mathbb{R}^{p}$ observed at irregularly spaced locations
in $R_{n} =[0,A_{n}]^{d} \subset \mathbb{R}^{d}$. We first derive the uniform
convergence rate of general kernel estimators, followed by the asymptotic
normality of an estimator for the mean function of the model. Moreover, we
consider additive models to avoid the curse of dimensionality arising from the
dependence of the convergence rate of estimators on the number of covariates.
Subsequently, we derive the uniform convergence rate and joint asymptotic
normality of the estimators for additive functions. We also introduce
approximately $m_{n}$-dependent RFs to provide examples of LSRFs. We find that
these RFs include a wide class of L\'evy-driven moving average RFs.
