Weight Theory for Integral Transforms on Spaces of Homogeneous Type

Basic ingredients maximal functions in Lorentz spaces two weight inequalities for integral transforms with a positive kernel two weight inequalities of strong type for the fractional maximal function maximal functions in phi(L) classes weighted inequalities of weak type for the maximal function one weight inequalities of strong type for the maximal function in phi(l) classes weighted inequalities for singular integrals two weight inequalities for singular integrals on homogenous groups inequalities in weighted Morrey-Campanato spaces and BMO two weight imbedding theorems applications to some BVPs.