Page 1 Next

Displaying 1 – 20 of 71

Showing per page

Wavelet transform for functions with values in UMD spaces

Cornelia Kaiser, Lutz Weis (2008)

Studia Mathematica

We extend the classical theory of the continuous and discrete wavelet transform to functions with values in UMD spaces. As a by-product we obtain equivalent norms on Bochner spaces in terms of g-functions.

Weak- and strong-type inequality for the cone-like maximal operator in variable Lebesgue spaces

Kristóf Szarvas, Ferenc Weisz (2016)

Czechoslovak Mathematical Journal

The classical Hardy-Littlewood maximal operator is bounded not only on the classical Lebesgue spaces L p ( d ) (in the case p > 1 ), but (in the case when 1 / p ( · ) is log-Hölder continuous and p - = inf { p ( x ) : x d } > 1 ) on the variable Lebesgue spaces L p ( · ) ( d ) , too. Furthermore, the classical Hardy-Littlewood maximal operator is of weak-type ( 1 , 1 ) . In the present note we generalize Besicovitch’s covering theorem for the so-called γ -rectangles. We introduce a general maximal operator M s γ , δ and with the help of generalized Φ -functions, the strong- and weak-type...

Weak type estimates for operators of potential type

Richard Wheeden, Shiying Zhao (1996)

Studia Mathematica

We derive two-weight weak type estimates for operators of potential type in homogeneous spaces. The conditions imposed on the weights are testing conditions of the kind first studied by E. T. Sawyer [4]. We also give some applications to strong type estimates as well as to operators on half-spaces.

Weak-type inequalities for maximal operators acting on Lorentz spaces

Adam Osękowski (2014)

Banach Center Publications

We prove sharp a priori estimates for the distribution function of the dyadic maximal function ℳ ϕ, when ϕ belongs to the Lorentz space L p , q , 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 C p , q , r such that for any ϕ L p , q , | | ϕ | | r , C p , q , r | | ϕ | | p , q .

Weighted boundedness of Toeplitz type operators related to singular integral operators with non-smooth kernel

Xiaosha Zhou, Lanzhe Liu (2013)

Colloquium Mathematicae

Some weighted sharp maximal function inequalities for the Toeplitz type operator T b = k = 1 m T k , 1 M b T k , 2 are established, where T k , 1 are a fixed singular integral operator with non-smooth kernel or ±I (the identity operator), T k , 2 are linear operators defined on the space of locally integrable functions, k = 1,..., m, and M b ( f ) = b f . The weighted boundedness of T b on Morrey spaces is obtained by using sharp maximal function inequalities.

Weighted bounds for variational Fourier series

Yen Do, Michael Lacey (2012)

Studia Mathematica

For 1 < p < ∞ and for weight w in A p , we show that the r-variation of the Fourier sums of any function f in L p ( w ) is finite a.e. for r larger than a finite constant depending on w and p. The fact that the variation exponent depends on w is necessary. This strengthens previous work of Hunt-Young and is a weighted extension of a variational Carleson theorem of Oberlin-Seeger-Tao-Thiele-Wright. The proof uses weighted adaptation of phase plane analysis and a weighted extension of a variational inequality...

Weighted endpoint estimates for commutators of fractional integrals

David Cruz-Uribe, Alberto Fiorenza (2007)

Czechoslovak Mathematical Journal

Given α , 0 < α < n , and b B M O , we give sufficient conditions on weights for the commutator of the fractional integral operator, [ b , I α ] , to satisfy weighted endpoint inequalities on n and on bounded domains. These results extend our earlier work [3], where we considered unweighted inequalities on n .

Weighted endpoint estimates for commutators of multilinear fractional integral operators

Xuefang Yan, Limei Xue, Wenming Li (2012)

Czechoslovak Mathematical Journal

Let m be a positive integer, 0 < α < m n , b = ( b 1 , , b m ) BMO m . We give sufficient conditions on weights for the commutators of multilinear fractional integral operators α b to satisfy a weighted endpoint inequality which extends the result in D. Cruz-Uribe, A. Fiorenza: Weighted endpoint estimates for commutators of fractional integrals, Czech. Math. J. 57 (2007), 153–160. We also give a weighted strong type inequality which improves the result in X. Chen, Q. Xue: Weighted estimates for a class of multilinear fractional type...

Weighted estimates for commutators of linear operators

Josefina Alvarez, Richard Bagby, Douglas Kurtz, Carlos Pérez (1993)

Studia Mathematica

We study boundedness properties of commutators of general linear operators with real-valued BMO functions on weighted L p spaces. We then derive applications to particular important operators, such as Calderón-Zygmund type operators, pseudo-differential operators, multipliers, rough singular integrals and maximal type operators.

Currently displaying 1 – 20 of 71

Page 1 Next