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We first introduce some new Morrey type spaces containing generalized Morrey space and weighted Morrey space as special cases. Then, we discuss the strong-type and weak-type estimates for a class of Calderón–Zygmund type operators Tθ in these new Morrey type spaces. Furthermore, the strong-type estimate and endpoint estimate of commutators [b,Tθ] formed by b and Tθ are established. Also, we study related problems about two-weight, weak-type inequalities for Tθ and [b,Tθ] in the Morrey type spaces and give partial results

journal of function spaces

Boundedness of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>θ</mml:mi></mml:mrow></mml:math>-Type Calderón–Zygmund Operators and Commutators in the Generalized Weighted Morrey Spaces

Boundedness ofθ-Type Calderón–Zygmund Operators and Commutators in the Generalized Weighted Morrey Spaces