The weak type inequality for the Walsh system
Ushangi Goginava (2008)
Studia Mathematica
Similarity:
The main aim of this paper is to prove that the maximal operator is bounded from the Hardy space to weak- and is not bounded from to .
Ushangi Goginava (2008)
Studia Mathematica
Similarity:
The main aim of this paper is to prove that the maximal operator is bounded from the Hardy space to weak- and is not bounded from to .
Milan Pokorný (1996)
Applications of Mathematics
Similarity:
We study the Cauchy problem for the non-Newtonian incompressible fluid with the viscous part of the stress tensor , where the nonlinear function satisfies or . First, the model for the bipolar fluid is studied and existence, uniqueness and regularity of the weak solution is proved for for both models. Then, under vanishing higher viscosity , the Cauchy problem for the monopolar fluid is considered. For the first model the existence of the weak solution is proved for , its uniqueness...
Fabio Berra (2022)
Czechoslovak Mathematical Journal
Similarity:
We give a quantitative characterization of the pairs of weights for which the dyadic version of the one-sided Hardy-Littlewood maximal operator satisfies a restricted weak type inequality for . More precisely, given any measurable set , the estimate holds if and only if the pair belongs to , that is, for every dyadic cube and every measurable set . The proof follows some ideas appearing in S. Ombrosi (2005). We also obtain a similar quantitative characterization for the...
Kristóf Szarvas, Ferenc Weisz (2016)
Czechoslovak Mathematical Journal
Similarity:
The classical Hardy-Littlewood maximal operator is bounded not only on the classical Lebesgue spaces (in the case ), but (in the case when is log-Hölder continuous and ) on the variable Lebesgue spaces , too. Furthermore, the classical Hardy-Littlewood maximal operator is of weak-type . In the present note we generalize Besicovitch’s covering theorem for the so-called -rectangles. We introduce a general maximal operator and with the help of generalized -functions, the strong-...
Adam Osękowski (2014)
Banach Center Publications
Similarity:
We prove sharp a priori estimates for the distribution function of the dyadic maximal function ℳ ϕ, when ϕ belongs to the Lorentz space , 1 < p < ∞, 1 ≤ q < ∞. The approach rests on a precise evaluation of the Bellman function corresponding to the problem. As an application, we establish refined weak-type estimates for the dyadic maximal operator: for p,q as above and r ∈ [1,p], we determine the best constant such that for any , .
Tobias Nau (2015)
Czechoslovak Mathematical Journal
Similarity:
In this article we prove for the existence of the -Helmholtz projection in finite cylinders . More precisely, is considered to be given as the Cartesian product of a cube and a bounded domain having -boundary. Adapting an approach of Farwig (2003), operator-valued Fourier series are used to solve a related partial periodic weak Neumann problem. By reflection techniques the weak Neumann problem in is solved, which implies existence and a representation of the -Helmholtz projection...
Peixin Zhang, Mingxuan Zhu (2022)
Applications of Mathematics
Similarity:
We establish the local-in-time existence of a solution to the non-resistive magneto-micropolar fluids with the initial data , and for and any . The initial regularity of the micro-rotational velocity is weaker than velocity of the fluid .
Salvador García-Ferreira, Y. F. Ortiz-Castillo (2015)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
Let be the subspace of consisting of all weak -points. It is not hard to see that is a pseudocompact space. In this paper we shall prove that this space has stronger pseudocompact properties. Indeed, it is shown that is a -pseudocompact space for all .
Jiecheng Chen, Dashan Fan, Yiming Ying (2002)
Studia Mathematica
Similarity:
We give some rather weak sufficient condition for boundedness of the Marcinkiewicz integral operator on the product spaces (1 < p < ∞), which improves and extends some known results.
Jorg Wolf (2007)
Bollettino dell'Unione Matematica Italiana
Similarity:
In the present work we prove the interior Hölder continuity of the gradient matrix of any weak solution of equations, which describes the motion of non-Newtonian fluid in two dimensions, restricting ourself to the shear thinning case .