Abstract
Suppose that d ≥ 1 is an integer, \({\alpha \in (0,d)}\) is a fixed parameter and let I α be the fractional integral operator associated with d-dimensional Walsh–Fourier series on [0, 1)d. The paper contains the proof of the sharp weak-type estimate
The proof rests on Bellman-function-type method: the above estimate is deduced from the existence of a certain family of special functions.
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Osȩkowski, A. Sharp Weak Type Inequality for Fractional Integral Operators Associated with d-Dimensional Walsh–Fourier Series. Integr. Equ. Oper. Theory 78, 589–600 (2014). https://doi.org/10.1007/s00020-013-2116-7
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DOI: https://doi.org/10.1007/s00020-013-2116-7