Potentials on RN
In this chapter we develop a new approach to truncated potentials. We introduce the extension of truncated potentials and prove necessary and sufficient conditions for boundedness from L p (R n ) into L v q (R n ), when 1 < p < ∞, 0 < q < ∞ and α > n/p. A generalization of Sawyer’s result  is presented. Then a compactness criterion for this operator is proved, and upper and lower estimates of its distance from the class of compact operators are derived.
KeywordsCompact Operator Riesz Potential Positive Borel Measure Radial Kernel Weak Type Inequality
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