A Note on Multiplication and Composition Operators in Lorentz Spaces

we revisit the Lorentz spaces (,) for >1,>0 defined by G. G. Lorentz in the nineteen fifties and we show how the atomic decomposition of the spaces (,1) obtained by De Souza in 2010 can be used to characterize the multiplication and composition operators on these spaces. These characterizations, though obtained from a completely different perspective, confirm the various results obtained by S. C. Arora, G. Datt and S. Verma in different variants of the Lorentz Spaces.