Sparse Operators and their boundedness on Morrey-type Spaces: An Expository Note

Sparse domination is a central tool in modern harmonic analysis, offering a unified approach to weighted inequalities for Calderón–Zygmund operators and related operators such as commutator operators, rough singular integrals, square functions etc. In this expository note, we briefly survey the main ideas behind sparse bounds on $L^p$ and weighted $L^p$ spaces, and discuss boundedness results for sparse operators on Morrey and generalized Morrey spaces. We establish a model result on the boundedness of sparse operators on Komori–Shirai type weighted Morrey spaces $L^{p,\kappa }(w)$, $w\in A_p$. These bounds offer a simpler framework for deriving Morrey-space estimates for Calderón–Zygmund operators and related operators via sparse domination. We conclude with remarks about extensions and connections to other Morrey space settings.