On the Boundedness of Classical Operators on Weighted Lorentz Spaces

  title={On the Boundedness of Classical Operators on Weighted Lorentz Spaces},
  author={Yves Rakotondratsimba},
Conditions on weights u(·), v(·) are given so that a classical operator T sends the weighted Lorentz space Lrs(vdx) into Lpq(udx). Here T is either a fractional maximal operator Mα or a fractional integral operator Iα or a Calderón–Zygmund operator. A characterization of this boundedness is obtained for Mα and Iα when the weights have some usual properties and max(r, s) ≤ min(p, q). § 0. Introduction Let u(·), v(·), w1(·), w2(·) be weight functions on Rn, n ∈ N∗, i.e., nonnegative locally… CONTINUE READING

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