Kernel operators on the upper half-space: boundedness and compactness criteria

Authors: USMAN ASHRAF, MUHAMMAD ASIF, ALEXANDER MESKHI

Abstract: We establish necessary and sufficient conditions on a weight v governing the trace inequality |\hat{K}f|_{L^q_v(\hat{E})} \leq C|f|_{L^p(E)}, where E is a cone on a homogeneous group, \hat{E}: = E \times R_+ and \hat{K} is a positive kernel operator defined on \hat{E}. Compactness criteria for this operator are also established.

Keywords: Operators with positive kernels, upper half-space, potentials, homogeneous groups, trace inequality, boundedness, compactness, weights

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