Recent progress in the study of the boundedness of classical operators of real analysis in general Morrey-type spaces

Let $0 <p, \theta \le \infty$ and let $w$ be a non-negative measurable function on $(0,\infty)$. We denote by $LM_{p\theta,w}$, $GM_{p\theta,w}$, the local Morrey-type spaces, the global Morrey-type spaces respectively, which are the spaces of all functions $f\in L_p^{loc}(\mathbb{R}^n)$ with finite quasi-norms
$$ \bigl\|w(r)\|f\|_{L_p({B_r})} \bigr\|_{L_\theta(0,\infty)},\qquad \sup_{x\in \mathbb{R}^n }\|f(x+\,\cdot\,)\|_{LM_{p\theta,w}} $$
respectively. (Here ${B_r}$ is the ball of radius $r$ centered at the origin.) For $w(r)=r^{-\frac\lambda p}$ with $0<\lambda<n$ the spaces $GM_{p\theta,w}$ were introduced by C. Morrey in 1938 and appeared to be quite useful in various problems in the theory of partial differential equations.
A survey will be given of recent results in which, for a certain range of the numerical parameters $p_1$, $\theta_1$, $p_2$, $\theta_2$, necessary and sufficient conditions on the functions $w_1$ and $w_2$ are established ensuring the boundedness of the maximal operator, fractional maximal operator, Riesz potential, genuine singular integrals, the Hardy operator as operators from one local Morrey-type space $LM_{p_1\theta_1,w_1}$ to another one $LM_{p_2\theta_2,w_2}$.
Under discussion there will also be interpolation theorems for general local Morrey-type spaces $LM_{p\theta,w}$.