  This note investigates the explicit convergence rates of nonlocal peridynamic
operators to their classical (local) counterparts in $L^q$-norm. Previous
results used Fourier series and hence were restricted to showing convergence in
$L^2$. Moreover, convergence rates were not explicit due to the use of the
Lebesgue Dominated Convergence Theorem. Some previous results have also used
the Taylor Remainder Theorem in differential form, but this often required an
assumption of bounded fifth-order derivatives. We do not use these tools, but
instead use the Hardy-Littlewood Maximal function, and combine it with the
integral form of the Taylor Remainder Theorem. This approach allows us to
establish convergence in the $L^q$-norm ($1 \leq q \leq \infty$) for nonlocal
peridynamic partial derivatives, which immediately yields convergence rates for
the corresponding nonlocal peridynamic divergence, gradient, and curl operators
to their local counterparts as the radius (a.k.a., ``horizon'') of the nonlocal
interaction $\delta \to 0$. Moreover, we obtain an explicit rate of order
$\mathcal{O}(\delta^2)$. This result contributes to the understanding of the
relationship between nonlocal and local models, which is essential for
applications in multiscale modeling and simulations.
