Joaquin M. Ortega

Wolff's Inequality for Radially Nonincreasing Kernels and Applications to Trace Inequalities

AbstractWe extend Th. Wolffs inequality to a general class of radially decreasing convolution kernels. As an application we obtain characterizations of nonnegative Borel measures μ on Rn such that the trace inequality

Imbedding potentials in tent spaces

\parallel {\kern 1pt} T_K f{\kern 1pt} \parallel _{L^q ({\text{d}}\mu )} \;\; \leqslant \;\;C\parallel {\kern 1pt} f{\kern 1pt} \parallel _{L^p ({\text{d}}x)}

On

holds for every f in Lp(dx).

\lowercase{q}

We give necessary and sufficient conditions in order that inequalities of the type \[ \| T_K f\|_{L^q(d\mu)}\leq C \|f\|_{L^p(d\sigma)}, \quad f \in L^p(d\sigma), \] hold for a class of integral operators

-Carleson measures for spaces of

T_K f(x) = \int_{R^n} K(x,y) f(y)\,d \sigma(y)

{\cal M}

with nonnegative kernels, and measures

-harmonic functions

d \mu

TWO-WEIGHT NORM INEQUALITIES FOR VECTOR-VALUED OPERATORS

and