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Displaying similar documents to “Polyanalytic Besov spaces and approximation by dilatations”

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. ...

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.

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.

Weighted w -core inverses in rings

Liyun Wu, Huihui Zhu (2023)

Czechoslovak Mathematical Journal

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Let R be a unital * -ring. For any a , s , t , v , w R we define the weighted w -core inverse and the weighted dual s -core inverse, extending the w -core inverse and the dual s -core inverse, respectively. An element a R has a weighted w -core inverse with the weight v if there exists some x R such that a w x v x = x , x v a w a = a and ( a w x ) * = a w x . Dually, an element a R has a weighted dual s -core inverse with the weight t if there exists some y R such that y t y s a = y , a s a t y = a and ( y s a ) * = y s a . Several characterizations of weighted w -core invertible and weighted dual s -core...

Note on duality of weighted multi-parameter Triebel-Lizorkin spaces

Wei Ding, Jiao Chen, Yaoming Niu (2019)

Czechoslovak Mathematical Journal

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We study the duality theory of the weighted multi-parameter Triebel-Lizorkin spaces F ˙ p α , q ( ω ; n 1 × n 2 ) . This space has been introduced and the result ( F ˙ p α , q ( ω ; n 1 × n 2 ) ) * = CMO p - α , q ' ( ω ; n 1 × n 2 ) for 0 < p 1 has been proved in Ding, Zhu (2017). In this paper, for 1 < p < , 0 < q < we establish its dual space H ˙ p α , q ( ω ; n 1 × n 2 ) .

A note on the weighted Khintchine-Groshev Theorem

Mumtaz Hussain, Tatiana Yusupova (2014)

Journal de Théorie des Nombres de Bordeaux

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Let W ( m , n ; ψ ̲ ) denote the set of ψ 1 , ... , ψ n –approximable points in m n . The classical Khintchine–Groshev theorem assumes a monotonicity condition on the approximating functions ψ ̲ . Removing monotonicity from the Khintchine–Groshev theorem is attributed to different authors for different cases of m and n . It can not be removed for m = n = 1 as Duffin–Schaeffer provided the counter example. We deal with the only remaining case m = 2 and thereby remove all unnecessary conditions from the Khintchine–Groshev theorem. ...

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 ) .

On the approximation of real continuous functions by series of solutions of a single system of partial differential equations

Carsten Elsner (2006)

Colloquium Mathematicae

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We prove the existence of an effectively computable integer polynomial P(x,t₀,...,t₅) having the following property. Every continuous function f : s can be approximated with arbitrary accuracy by an infinite sum r = 1 H r ( x , . . . , x s ) C ( s ) of analytic functions H r , each solving the same system of universal partial differential equations, namely P ( x σ ; H r , H r / x σ , . . . , H r / x σ ) = 0 (σ = 1,..., s).

Embeddings between weighted Copson and Cesàro function spaces

Amiran Gogatishvili, Rza Mustafayev, Tuğçe Ünver (2017)

Czechoslovak Mathematical Journal

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In this paper, characterizations of the embeddings between weighted Copson function spaces Cop p 1 , q 1 ( u 1 , v 1 ) and weighted Cesàro function spaces Ces p 2 , q 2 ( u 2 , v 2 ) are given. In particular, two-sided estimates of the optimal constant c in the inequality d ( 0 0 t f ( τ ) p 2 v 2 ( τ ) d τ q 2 / p 2 u 2 ( t ) d t ) 1 / q 2 c 0 t f ( τ ) p 1 v 1 ( τ ) d τ q 1 / p 1 u 1 ( t ) d t 1 / q 1 , d where p 1 , p 2 , q 1 , q 2 ( 0 , ) , p 2 q 2 and u 1 , u 2 , v 1 , v 2 are weights on ( 0 , ) , are obtained. The most innovative part consists of the fact that possibly different parameters p 1 and p 2 and possibly different inner weights v 1 and v 2 are allowed. The proof is based on the combination of duality techniques...

The norm of the polynomial truncation operator on the unit disk and on [-1,1]

Tamás Erdélyi (2001)

Colloquium Mathematicae

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Let D and ∂D denote the open unit disk and the unit circle of the complex plane, respectively. We denote by ₙ (resp. c ) the set of all polynomials of degree at most n with real (resp. complex) coefficients. We define the truncation operators Sₙ for polynomials P c of the form P ( z ) : = j = 0 n a j z j , a j C , by S ( P ) ( z ) : = j = 0 n a ̃ j z j , a ̃ j : = a j | a j | m i n | a j | , 1 (here 0/0 is interpreted as 1). We define the norms of the truncation operators by S , D r e a l : = s u p P ( m a x z D | S ( P ) ( z ) | ) / ( m a x z D | P ( z ) | ) , S , D c o m p : = s u p P c ( m a x z D | S ( P ) ( z ) | ) / ( m a x z D | P ( z ) | . Our main theorem establishes the right order of magnitude of the above norms: there is an absolute constant c₁...

On the multiples of a badly approximable vector

Yann Bugeaud (2015)

Acta Arithmetica

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Let d be a positive integer and α a real algebraic number of degree d + 1. Set α ̲ : = ( α , α ² , . . . , α d ) . It is well-known that c ( α ̲ ) : = l i m i n f q q 1 / d · | | q α ̲ | | > 0 , where ||·|| denotes the distance to the nearest integer. Furthermore, c ( α ̲ ) n - 1 / d c ( n α ̲ ) n c ( α ̲ ) for any integer n ≥ 1. Our main result asserts that there exists a real number C, depending only on α, such that c ( n α ̲ ) C n - 1 / d for any integer n ≥ 1.

Three-space problems for the approximation property

A. Szankowski (2009)

Journal of the European Mathematical Society

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It is shown that there is a subspace Z q of q for 1 < q < 2 which is isomorphic to q such that q / Z q does not have the approximation property. On the other hand, for 2 < p < there is a subspace Y p of p such that Y p does not have the approximation property (AP) but the quotient space p / Y p is isomorphic to p . The result is obtained by defining random “Enflo-Davie spaces” Y p which with full probability fail AP for all 2 < p and have AP for all 1 p 2 . For 1 < p 2 , Y p are isomorphic to p .

Convexities of Gaussian integral means and weighted integral means for analytic functions

Haiying Li, Taotao Liu (2019)

Czechoslovak Mathematical Journal

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We first show that the Gaussian integral means of f : (with respect to the area measure e - α | z | 2 d A ( z ) ) is a convex function of r on ( 0 , ) when α 0 . We then prove that the weighted integral means A α , β ( f , r ) and L α , β ( f , r ) of the mixed area and the mixed length of f ( r 𝔻 ) and f ( r 𝔻 ) , respectively, also have the property of convexity in the case of α 0 . Finally, we show with examples that the range α 0 is the best possible.

Rademacher functions in Cesàro type spaces

Sergei V. Astashkin, Lech Maligranda (2010)

Studia Mathematica

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The Rademacher sums are investigated in the Cesàro spaces C e s p (1 ≤ p ≤ ∞) and in the weighted Korenblyum-Kreĭn-Levin spaces K p , w on [0,1]. They span l₂ space in C e s p for any 1 ≤ p < ∞ and in K p , w if and only if the weight w is larger than t l o g p / 2 ( 2 / t ) on (0,1). Moreover, the span of the Rademachers is not complemented in C e s p for any 1 ≤ p < ∞ or in K 1 , w for any quasi-concave weight w. In the case when p > 1 and when w is such that the span of the Rademacher functions is isomorphic to l₂, this span is...

Fourier approximation and embeddings of Sobolev spaces

D. E. Edmunds, V. B. Moscatelli

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CONTENTSIntroduction............................................................................................................ 51. Preliminaries............................................................................................................. 82. Embedding into W m , p ( Ω ) into L S ( Ω ) (n>1).......................................... 103. The case n = 1.......................................................................................................... 284. Embedding W m , p ( Ω ) into L φ ( Ω ) ...............................................................

Double weighted commutators theorem for pseudo-differential operators with smooth symbols

Yu-long Deng, Zhi-tian Chen, Shun-chao Long (2021)

Czechoslovak Mathematical Journal

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Let - ( n + 1 ) < m - ( n + 1 ) ( 1 - ρ ) and let T a ρ , δ m be pseudo-differential operators with symbols a ( x , ξ ) n × n , where 0 < ρ 1 , 0 δ < 1 and δ ρ . Let μ , λ be weights in Muckenhoupt classes A p , ν = ( μ λ - 1 ) 1 / p for some 1 < p < . We establish a two-weight inequality for commutators generated by pseudo-differential operators T a with weighted BMO functions b BMO ν , namely, the commutator [ b , T a ] is bounded from L p ( μ ) into L p ( λ ) . Furthermore, the range of m can be extended to the whole m - ( n + 1 ) ( 1 - ρ ) .