Abstract In this article, we study the following noncoercive quasilinear parabolic problem ∂ u t − div<...

We give a constructive proof of the factorization theorem for classical Hardy space in terms fractional integral operator. Moreover, result is extended to multilinear case and weighted case. As an application, we obtain characterization BMO via boundedness commutators operator, without individual conditions on weights class.

Abstract We formulate a generalization of Riesz-type criteria in the setting L -functions belonging to Selberg class. obtain criterion which is sufficient for grand Riemann hypothesis (GRH) satisfying axioms class without imposing Ramanujan on their coefficients. also construct subclass and prove necessary GRH this subclass. Identities Ramanujan–Hardy–Littlewood type are established setting, sp...

In this note, we obtain a simpler expression for the constant number given by Costin–Maz’ya on sharp Hardy–Leray inequality class of solenoidal (namely divergence-free) vector fields, with respect to any radial power-weighted measure. The dependence weight exponent will be clear.

The operator-valued Schur-class is defined to be the set of holomorphic functions S mapping the unit disk into the space of contraction operators between two Hilbert spaces. There are a number of alternate characterizations: the operator of multiplication by S defines a contraction operator between two Hardy Hilbert spaces, S satisfies a von Neumann inequality, a certain operator-valued kernel ...

We obtain Fourier inequalities in the weighted Lp spaces for any 1<p<∞ involving Hardy–Cesàro and Hardy–Bellman operators. extend these results to product Hardy p⩽1. Moreover, boundedness of Hardy-Cesàro Hardy-Bellman operators various (Lebesgue, Hardy, BMO) is discussed. One our main tools an appropriate version Hardy–Littlewood–Paley inequality ‖fˆ‖Lp′,q≲‖f‖Lp,q.

In this paper, the structural properties of a function are characterized by moduli continuity. The classical Hardy–Littlewood theorem describes relation between smoothness analytic boundary values at its analyticity and growth rate modulus higher-order derivatives. An analogue has been obtained for functions from class Hp