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Search: All articles in the CMB digital archive with keyword maximal operator

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1. CMB 2012 (vol 56 pp. 801)

Oberlin, Richard
 Estimates for Compositions of Maximal Operators with Singular Integrals We prove weak-type $(1,1)$ estimates for compositions of maximal operators with singular integrals. Our main object of interest is the operator $\Delta^*\Psi$ where $\Delta^*$ is Bourgain's maximal multiplier operator and $\Psi$ is the sum of several modulated singular integrals; here our method yields a significantly improved bound for the $L^q$ operator norm when $1 \lt q \lt 2.$ We also consider associated variation-norm estimates. Keywords:maximal operator calderon-zygmundCategory:42A45

2. CMB 2010 (vol 53 pp. 690)

Puerta, M. E.; Loaiza, G.
 On the Maximal Operator Ideal Associated with a Tensor Norm Defined by Interpolation Spaces The classical approach to studying operator ideals using tensor norms mainly focuses on those tensor norms and operator ideals defined by means of $\ell_p$ spaces. In a previous paper, an interpolation space, defined via the real method and using $\ell_p$ spaces, was used to define a tensor norm, and the associated minimal operator ideals were characterized. In this paper, the next natural step is taken, that is, the corresponding maximal operator ideals are characterized. As an application, necessary and sufficient conditions for the coincidence of the maximal and minimal ideals are given. Finally, the previous results are used in order to find some new metric properties of the mentioned tensor norm. Keywords:maximal operator ideals, ultraproducts of spaces, interpolation spacesCategories:46M05, 46M35, 46A32

3. CMB 2009 (vol 53 pp. 263)

Feuto, Justin; Fofana, Ibrahim; Koua, Konin
 Weighted Norm Inequalities for a Maximal Operator in Some Subspace of Amalgams We give weighted norm inequalities for the maximal fractional operator $\mathcal M_{q,\beta }$ of HardyÂLittlewood and the fractional integral $I_{\gamma}$. These inequalities are established between $(L^{q},L^{p}) ^{\alpha }(X,d,\mu )$ spaces (which are superspaces of Lebesgue spaces $L^{\alpha}(X,d,\mu)$ and subspaces of amalgams $(L^{q},L^{p})(X,d,\mu)$) and in the setting of space of homogeneous type $(X,d,\mu)$. The conditions on the weights are stated in terms of Orlicz norm. Keywords:fractional maximal operator, fractional integral, space of homogeneous typeCategories:42B35, 42B20, 42B25

4. CMB 1997 (vol 40 pp. 169)

Cruz-Uribe, David
 The class $A^{+}_{\infty}(\lowercase{g})$ and the one-sided reverse HÃ¶lder inequality We give a direct proof that $w$ is an $A^{+}_{\infty}(g)$ weight if and only if $w$ satisfies a one-sided, weighted reverse H\"older inequality. Keywords:one-sided maximal operator, one-sided $(A_\infty)$, one-sided, reverse HÃ¶lder inequalityCategory:42B25

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