Ascent and descent of weighted composition operators on Lorentz spaces

The aim of this article is to detect the ascent and descent of weighted composition operators on Lorentz spaces. We investigate the conditions on a measurable transformation T and a complex-valued measurable function u defined on a measure space $$(X,\mathcal {A},\mu )$$ that cause the weighted composition operators on Lorentz space L(p, q), $$1<p\le \infty $$ , $$1\le q\le \infty $$ to have finite or infinite ascent (descent). We also give a number of examples to illustrate our findings.