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Displaying similar documents to “Behaviour of L r -Dini singular integrals in weighted L 1 spaces”

Commutators on ( q ) p

Dongyang Chen, William B. Johnson, Bentuo Zheng (2011)

Studia Mathematica

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Let T be a bounded linear operator on X = ( q ) p with 1 ≤ q < ∞ and 1 < p < ∞. Then T is a commutator if and only if for all non-zero λ ∈ ℂ, the operator T - λI is not X-strictly singular.

Weighted norm inequalities for maximal singular integrals with nondoubling measures

Guoen Hu, Dachun Yang (2008)

Studia Mathematica

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Let μ be a nonnegative Radon measure on d which satisfies μ(B(x,r)) ≤ Crⁿ for any x d and r > 0 and some positive constants C and n ∈ (0,d]. In this paper, some weighted norm inequalities with A p ϱ ( μ ) weights of Muckenhoupt type are obtained for maximal singular integral operators with such a measure μ, via certain weighted estimates with A ϱ ( μ ) weights of Muckenhoupt type involving the John-Strömberg maximal operator and the John-Strömberg sharp maximal operator, where ϱ,p ∈ [1,∞).

A singular initial value problem for the equation u ( n ) ( x ) = g ( u ( x ) )

Wojciech Mydlarczyk (1998)

Annales Polonici Mathematici

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We consider the problem of the existence of positive solutions u to the problem u ( n ) ( x ) = g ( u ( x ) ) , u ( 0 ) = u ' ( 0 ) = . . . = u ( n - 1 ) ( 0 ) = 0 (g ≥ 0,x > 0, n ≥ 2). It is known that if g is nondecreasing then the Osgood condition δ 1 / s [ s / g ( s ) ] 1 / n d s < is necessary and sufficient for the existence of nontrivial solutions to the above problem. We give a similar condition for other classes of functions g.

Corrigendum to “Commutators on ( q ) p ” (Studia Math. 206 (2011), 175-190)

Dongyang Chen, William B. Johnson, Bentuo Zheng (2014)

Studia Mathematica

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We give a corrected proof of Theorem 2.10 in our paper “Commutators on ( q ) p ” [Studia Math. 206 (2011), 175-190] for the case 1 < q < p < ∞. The case when 1 = q < p < ∞ remains open. As a consequence, the Main Theorem and Corollary 2.17 in that paper are only valid for 1 < p,q < ∞.

Weighted estimates for the iterated commutators of multilinear maximal and fractional type operators

Qingying Xue (2013)

Studia Mathematica

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The following iterated commutators T , Π b of the maximal operator for multilinear singular integral operators and I α , Π b of the multilinear fractional integral operator are introduced and studied: T , Π b ( f ) ( x ) = s u p δ > 0 | [ b , [ b , [ b m - 1 , [ b , T δ ] ] m - 1 ] ] ( f ) ( x ) | , I α , Π b ( f ) ( x ) = [ b , [ b , [ b m - 1 , [ b , I α ] ] m - 1 ] ] ( f ) ( x ) , where T δ are the smooth truncations of the multilinear singular integral operators and I α is the multilinear fractional integral operator, b i B M O for i = 1,…,m and f⃗ = (f1,…,fm). Weighted strong and L(logL) type end-point estimates for the above iterated commutators associated with two classes of multiple...

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

Xiaosha Zhou, Lanzhe Liu (2013)

Colloquium Mathematicae

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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.

Common zero sets of equivalent singular inner functions

Keiji Izuchi (2004)

Studia Mathematica

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Let μ and λ be bounded positive singular measures on the unit circle such that μ ⊥ λ. It is proved that there exist positive measures μ₀ and λ₀ such that μ₀ ∼ μ, λ₀ ∼ λ, and | ψ μ | < 1 | ψ λ | < 1 = , where ψ μ is the associated singular inner function of μ. Let ( μ ) = ν ; ν μ Z ( ψ ν ) be the common zeros of equivalent singular inner functions of ψ μ . Then (μ) ≠ ∅ and (μ) ∩ (λ) = ∅. It follows that μ ≪ λ if and only if (μ) ⊂ (λ). Hence (μ) is the set in the maximal ideal space of H which relates naturally to the set of measures equivalent...

Boundedness of para-product operators on spaces of homogeneous type

Yayuan Xiao (2017)

Czechoslovak Mathematical Journal

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We obtain the boundedness of Calderón-Zygmund singular integral operators T of non-convolution type on Hardy spaces H p ( 𝒳 ) for 1 / ( 1 + ϵ ) < p 1 , where 𝒳 is a space of homogeneous type in the sense of Coifman and Weiss (1971), and ϵ is the regularity exponent of the kernel of the singular integral operator T . Our approach relies on the discrete Littlewood-Paley-Stein theory and discrete Calderón’s identity. The crucial feature of our proof is to avoid atomic decomposition and molecular theory in contrast...

Some weighted norm inequalities for a one-sided version of g * λ

L. de Rosa, C. Segovia (2006)

Studia Mathematica

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We study the boundedness of the one-sided operator g λ , φ between the weighted spaces L p ( M ¯ w ) and L p ( w ) for every weight w. If λ = 2/p whenever 1 < p < 2, and in the case p = 1 for λ > 2, we prove the weak type of g λ , φ . For every λ > 1 and p = 2, or λ > 2/p and 1 < p < 2, the boundedness of this operator is obtained. For p > 2 and λ > 1, we obtain the boundedness of g λ , φ from L p ( ( M ¯ ) [ p / 2 ] + 1 w ) to L p ( w ) , where ( M ¯ ) k denotes the operator M¯ iterated k times.

L p type mapping estimates for oscillatory integrals in higher dimensions

G. Sampson (2006)

Studia Mathematica

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We show in two dimensions that if K f = ² k ( x , y ) f ( y ) d y , k ( x , y ) = ( e i x a · y b ) / ( | x - y | η ) , p = 4/(2+η), a ≥ b ≥ 1̅ = (1,1), v p ( y ) = y ( p / p ' ) ( 1 ̅ - b / a ) , then | | K f | | p C | | f | | p , v p if η + α₁ + α₂ < 2, α j = 1 - b j / a j , j = 1,2. Our methods apply in all dimensions and also for more general kernels.

Multiplication operators on L ( L p ) and p -strictly singular operators

William Johnson, Gideon Schechtman (2008)

Journal of the European Mathematical Society

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A classification of weakly compact multiplication operators on L ( L p ) , 1<p< , i s g i v e n . T h i s a n s w e r s a q u e s t i o n r a i s e d b y S a k s m a n a n d T y l l i i n 1992 . T h e c l a s s i f i c a t i o n i n v o l v e s t h e c o n c e p t o f p - s t r i c t l y s i n g u l a r o p e r a t o r s , a n d w e a l s o i n v e s t i g a t e t h e s t r u c t u r e o f g e n e r a l p - s t r i c t l y s i n g u l a r o p e r a t o r s o n Lp . T h e m a i n r e s u l t i s t h a t i f a n o p e r a t o r T o n Lp , 1<p<2 , i s p - s t r i c t l y s i n g u l a r a n d T|X i s a n i s o m o r p h i s m f o r s o m e s u b s p a c e X o f Lp , t h e n X e m b e d s i n t o Lr f o r a l l r<2 , b u t X n e e d n o t b e i s o m o r p h i c t o a H i l b e r t s p a c e . It is also shown that if T is convolution by a biased coin on L p of the Cantor group, 1 p < 2 , and T | X is an isomorphism for some reflexive subspace X of L p , then X is isomorphic to a Hilbert space. The case p = 1 answers a question asked by Rosenthal in 1976.

L p ( ) boundedness for the commutator of a homogeneous singular integral operator

Guoen Hu (2003)

Studia Mathematica

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The commutator of a singular integral operator with homogeneous kernel Ω(x)/|x|ⁿ is studied, where Ω is homogeneous of degree zero and has mean value zero on the unit sphere. It is proved that Ω L ( l o g L ) k + 1 ( S n - 1 ) is a sufficient condition for the kth order commutator to be bounded on L p ( ) for all 1 < p < ∞. The corresponding maximal operator is also considered.

Marcinkiewicz integrals on product spaces

H. Al-Qassem, A. Al-Salman, L. C. Cheng, Y. Pan (2005)

Studia Mathematica

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We prove the L p boundedness of the Marcinkiewicz integral operators μ Ω on n × × n k under the condition that Ω L ( l o g L ) k / 2 ( n - 1 × × n k - 1 ) . The exponent k/2 is the best possible. This answers an open question posed by Y. Ding.

Lacunary series in Q K spaces

Hasi Wulan, Kehe Zhu (2007)

Studia Mathematica

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Under mild conditions on the weight function K we characterize lacunary series in the so-called K spaces.

New characterizations for weighted composition operator from Zygmund type spaces to Bloch type spaces

Xin-Cui Guo, Ze-Hua Zhou (2015)

Czechoslovak Mathematical Journal

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Let u be a holomorphic function and ϕ a holomorphic self-map of the open unit disk 𝔻 in the complex plane. We provide new characterizations for the boundedness of the weighted composition operators u C ϕ from Zygmund type spaces to Bloch type spaces in 𝔻 in terms of u , ϕ , their derivatives, and ϕ n , the n -th power of ϕ . Moreover, we obtain some similar estimates for the essential norms of the operators u C ϕ , from which sufficient and necessary conditions of compactness of u C ϕ follows immediately. ...

Weighted H p spaces

José García-Cuerva

Similarity:

CONTENTSIntroduction.......................................................................................................................................................... 5Chapter I. Some preliminary lemmas............................................................................................................ 8Chapter II. Weighted H p spaces of analytic functions.......................................................................... 13 1. Behaviour at the boundary..........................................................................................................................

Controlling products of currents by higher powers of plurisubharmonic functions

Ahmad K. Al Abdulaali, Hassine El Mir (2020)

Czechoslovak Mathematical Journal

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We discuss the existence of the current g k T , k for positive and closed currents T and unbounded plurisubharmonic functions g . Furthermore, a new type of weighted Lelong number is introduced under the name of weight k Lelong number.

Global solvability in the parabolic-elliptic chemotaxis system with singular sensitivity and logistic source

Xiangdong Zhao (2024)

Czechoslovak Mathematical Journal

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We study the chemotaxis system with singular sensitivity and logistic-type source: u t = Δ u - χ · ( u v / v ) + r u - μ u k , 0 = Δ v - v + u under the non-flux boundary conditions in a smooth bounded domain Ω n , χ , r , μ > 0 , k > 1 and n 1 . It is shown with k ( 1 , 2 ) that the system possesses a global generalized solution for n 2 which is bounded when χ > 0 is suitably small related to r > 0 and the initial datum is properly small, and a global bounded classical solution for n = 1 .

The weighted Hardy spaces associated to self-adjoint operators and their duality on product spaces

Suying Liu, Minghua Yang (2018)

Czechoslovak Mathematical Journal

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Let L be a non-negative self-adjoint operator acting on L 2 ( n ) satisfying a pointwise Gaussian estimate for its heat kernel. Let w be an A r weight on n × n , 1 < r < . In this article we obtain a weighted atomic decomposition for the weighted Hardy space H L , w p ( n × n ) , 0 < p 1 associated to L . Based on the atomic decomposition, we show the dual relationship between H L , w 1 ( n × n ) and BMO L , w ( n × n ) .