A Short Note on Weak Estimation of Sharp Function
Mohd. Sarfaraz *
Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India.
M. K. Ahmad
Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India.
*Author to whom correspondence should be addressed.
Abstract
In paper [1] Ahmad et al. investigated the use of sharp function, known from functional analysis, in image processing. The sharp function gives a measure of variations of a function and can be used as an edge detector [2]. We extend the classical notion of sharp function to prove the classical Lebesgue differentiation theorem and Marcinkiewicz theorem for the sublinear operator T(x, y).
Keywords: Maximal function, bounded mean oscillations (BMO), sharp function, distribution, sublinear operator.