The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying 541 – 560 of 693

Showing per page

The higher order Riesz transform for Gaussian measure need not be of weak type (1,1)

Liliana Forzani, Roberto Scotto (1998)

Studia Mathematica

The purpose of this paper is to prove that the higher order Riesz transform for Gaussian measure associated with the Ornstein-Uhlenbeck differential operator L : = d 2 / d x 2 - 2 x d / d x , x ∈ ℝ, need not be of weak type (1,1). A function in L 1 ( d γ ) , where dγ is the Gaussian measure, is given such that the distribution function of the higher order Riesz transform decays more slowly than C/λ.

The John-Nirenberg inequality for functions of bounded mean oscillation with bounded negative part

Min Hu, Dinghuai Wang (2022)

Czechoslovak Mathematical Journal

A version of the John-Nirenberg inequality suitable for the functions b BMO with b - L is established. Then, equivalent definitions of this space via the norm of weighted Lebesgue space are given. As an application, some characterizations of this function space are given by the weighted boundedness of the commutator with the Hardy-Littlewood maximal operator.

The John-Nirenberg type inequality for non-doubling measures

Yoshihiro Sawano, Hitoshi Tanaka (2007)

Studia Mathematica

X. Tolsa defined a space of BMO type for positive Radon measures satisfying some growth condition on d . This new BMO space is very suitable for the Calderón-Zygmund theory with non-doubling measures. Especially, the John-Nirenberg type inequality can be recovered. In the present paper we introduce a localized and weighted version of this inequality and, as applications, we obtain some vector-valued inequalities and weighted inequalities for Morrey spaces.

The linear bound in A₂ for Calderón-Zygmund operators: a survey

Michael Lacey (2011)

Banach Center Publications

For an L²-bounded Calderón-Zygmund Operator T acting on L ² ( d ) , and a weight w ∈ A₂, the norm of T on L²(w) is dominated by C T | | w | | A . The recent theorem completes a line of investigation initiated by Hunt-Muckenhoupt-Wheeden in 1973 (MR0312139), has been established in different levels of generality by a number of authors over the last few years. It has a subtle proof, whose full implications will unfold over the next few years. This sharp estimate requires that the A₂ character of the weight can be exactly...

The maximal theorem for weighted grand Lebesgue spaces

Alberto Fiorenza, Babita Gupta, Pankaj Jain (2008)

Studia Mathematica

We study the Hardy inequality and derive the maximal theorem of Hardy and Littlewood in the context of grand Lebesgue spaces, considered when the underlying measure space is the interval (0,1) ⊂ ℝ, and the maximal function is localized in (0,1). Moreover, we prove that the inequality | | M f | | p ) , w c | | f | | p ) , w holds with some c independent of f iff w belongs to the well known Muckenhoupt class A p , and therefore iff | | M f | | p , w c | | f | | p , w for some c independent of f. Some results of similar type are discussed for the case of small Lebesgue spaces....

The minimal operator and the geometric maximal operator in ℝⁿ

David Cruz-Uribe, SFO (2001)

Studia Mathematica

We prove two-weight norm inequalities in ℝⁿ for the minimal operator f ( x ) = i n f Q x 1 / | Q | Q | f | d y , extending to higher dimensions results obtained by Cruz-Uribe, Neugebauer and Olesen [8] on the real line. As an application we extend to ℝⁿ weighted norm inequalities for the geometric maximal operator M f ( x ) = s u p Q x e x p ( 1 / | Q | Q l o g | f | d x ) , proved by Yin and Muckenhoupt [27]. We also give norm inequalities for the centered minimal operator, study powers of doubling weights and give sufficient conditions for the geometric maximal operator to be equal to the closely...

The minimal operator and the John--Nirenberg theorem for weighted grand Lebesgue spaces

Lihua Peng, Yong Jiao (2015)

Studia Mathematica

We introduce the minimal operator on weighted grand Lebesgue spaces, discuss some weighted norm inequalities and characterize the conditions under which the inequalities hold. We also prove that the John-Nirenberg inequalities in the framework of weighted grand Lebesgue spaces are valid provided that the weight function belongs to the Muckenhoupt A p class.

The Muckenhoupt class A₁(R)

B. Bojarski, C. Sbordone, I. Wik (1992)

Studia Mathematica

It is shown that the Muckenhoupt structure constants for f and f* on the real line are the same.

The one-sided minimal operator and the one-sided reverse Holder inequality

David Cruz-Uribe, SFO, C. Neugebauer, V. Olesen (1995)

Studia Mathematica

We introduce the one-sided minimal operator, m + f , which is analogous to the one-sided maximal operator. We determine the weight classes which govern its two-weight, strong and weak-type norm inequalities, and show that these two classes are the same. Then in the one-weight case we use this class to introduce a new one-sided reverse Hölder inequality which has several applications to one-sided ( A p + ) weights.

The solution of Kato's conjecture (after Auscher, Hofmann, Lacey, McIntosh and Tchamitchian)

Philippe Tchamitchian (2001)

Journées équations aux dérivées partielles

Kato’s conjecture, stating that the domain of the square root of any accretive operator L = - div ( A ) with bounded measurable coefficients in n is the Sobolev space H 1 ( n ) , i.e. the domain of the underlying sesquilinear form, has recently been obtained by Auscher, Hofmann, Lacey, McIntosh and the author. These notes present the result and explain the strategy of proof.

The space of maximal Fourier multipliers as a dual space

Naohito Tomita (2006)

Studia Mathematica

Figà-Talamanca characterized the space of Fourier multipliers as the dual space of a certain Banach space. In this paper, we characterize the space of maximal Fourier multipliers as a dual space.

Currently displaying 541 – 560 of 693