Θ-type Calderon-Zygmund Operators with Non-doubling Measures

Let mu be a Radon measure on R-d which may be non-doubling. The only condition that mu must satisfy is mu(B(x, r)) <= Cr-n for all x is an element of R-d, r > 0 and for some fixed 0 < n <= d. In this paper, under this assumption, we prove that theta-type Calderon-Zygmund operator which is bounded on L-2(mu) is also bounded from L-infinity(mu) into RBMO(mu) and from H-atb(1,infinity) (mu) into L-1(mu). According to the interpolation theorem introduced by Tolsa, the L-p(mu)-boundedness (1 < p < infinity) is established for theta-type Calderon-Zygmund operators. Via a sharp maximal operator, it is shown that commutators and multilinear commutators of theta-type Calderon-Zygmund operator with RBMO(mu) function are bounded on L-p(mu) (1 < p < infinity).