Titlebook: Special Functions, Partial Differential Equations, and Harmonic Analysis; In Honor of Calixto Constantine Georgakis,Alexander M. Stokolos,

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Solyanik Estimates in Harmonic Analysis,d by previous work of A. A. Solyanik, we show that if . is the uncentered Hardy–Littlewood maximal operator associated with balls, the estimate . holds. Similar results for iterated maximal functions are obtained, and open problems in the field of Solyanik estimates are also discussed.

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Towards a Unified Theory of Sobolev Inequalities, show how they can be used to unify certain aspects of the theory of Sobolev inequalities. In particular, we discuss our recent papers on fractional order inequalities, Coulhon type inequalities, transference and dimensionless inequalities and our forthcoming work on sharp higher order Sobolev inequalities that can be obtained by iteration.

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