Maximal and Calderón–Zygmund operators in grand variable exponent Lebesgue spaces

Abstract

Abstract New function spaces L p ( · ) , θ $L^{ p(\,\cdot \,), \theta }$ , ℒ p ( · ) , θ ${\mathcal {L}}^{ p(\,\cdot \,), \theta }$ unifying grand Lebesgue spaces and variable exponent Lebesgue spaces are introduced. The boundedness of maximal and Calderón–Zygmund operators in these spaces defined on spaces of homogeneous type are derived. The Sobolev type theorem for fractional integrals is also established in the class of functions which is narrower than the space L p ( · ) , θ $L^{ p(\,\cdot \,),\theta }$ .