scholarly journals Boundedness and Compactness of Hankel Operators on Large Fock Space

2022 ◽  
Vol 2022 ◽  
pp. 1-12
Author(s):  
Xiaofeng Wang ◽  
Zhicheng Zeng
Keyword(s):  
Lebesgue Space ◽  
Fock Space ◽  
Hankel Operators ◽  
Weighted Lebesgue Space ◽  
Bmo Spaces ◽  
Complex Valued

We introduce the BMO spaces and use them to characterize complex-valued functions f such that the big Hankel operators H f and H f ¯ are both bounded or compact from a weighted large Fock space F p ϕ into a weighted Lebesgue space L p ϕ when 1 ≤ p < ∞ .

Generalized Hankel operators on the Fock space II

2011 ◽  
Vol 284 (14-15) ◽  
pp. 1967-1984 ◽  
Author(s):  
Georg Schneider ◽  
Kristan Schneider
Keyword(s):  
Fock Space ◽  
Hankel Operators

Polynomial inequalities in regions with corners in theweighted Lebesgue spaces

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5647-5670 ◽  
Author(s):  
Fahreddin Abdullayev
Keyword(s):  
Orthogonal Polynomials ◽  
Lebesgue Space ◽  
Weight Functions ◽  
Weighted Lebesgue Space ◽  
Algebraic Polynomials ◽  
Lebesgue Spaces ◽  
Polynomial Inequalities

In this work, we investigate the order of the growth of the modulus of orthogonal polynomials over a contour and also arbitrary algebraic polynomials in regions with corners in a weighted Lebesgue space, where the singularities of contour and the weight functions satisfy some condition.

On multipliers of Fourier transforms

1972 ◽  
Vol 71 (1) ◽  
pp. 63-66 ◽  
Author(s):  
Louis Pigno
Keyword(s):  
Abelian Group ◽  
Haar Measure ◽  
Compact Abelian Group ◽  
Lebesgue Space ◽  
Fourier Transforms ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Continuous Complex ◽  
Complex Valued

In this paper G is a locally compact Abelian group, φ a complex-valued function defined on the dual Γ, Lp(G) (1 ≤ p ≤ ∞) the usual Lebesgue space of index p formed with respect to Haar measure, C(G) the set of all bounded continuous complex-valued functions on G, and C0(G) the set of all f ∈ C(G) which vanish at infinity.

scholarly journals Finite-rank intermediate Hankel operators on the Bergman space

2001 ◽  
Vol 25 (1) ◽  
pp. 19-31 ◽  
Author(s):  
Takahiko Nakazi ◽  
Tomoko Osawa
Keyword(s):  
Bergman Space ◽  
Orthogonal Projection ◽  
Finite Rank ◽  
Lebesgue Space ◽  
Unit Disc ◽  
Hankel Operator ◽  
Hankel Operators ◽  
Weighted Bergman Space ◽  
Open Unit ◽  
Open Unit Disc

LetL2=L2(D,r dr dθ/π)be the Lebesgue space on the open unit disc and letLa2=L2∩ℋol(D)be the Bergman space. LetPbe the orthogonal projection ofL2ontoLa2and letQbe the orthogonal projection ontoL¯a,02={g∈L2;g¯∈La2,   g(0)=0}. ThenI−P≥Q. The big Hankel operator and the small Hankel operator onLa2are defined as: forϕinL∞,Hϕbig(f)=(I−P)(ϕf)andHϕsmall(f)=Q(ϕf)(f∈La2). In this paper, the finite-rank intermediate Hankel operators betweenHϕbigandHϕsmallare studied. We are working on the more general space, that is, the weighted Bergman space.

scholarly journals On Variable Exponent Amalgam Spaces

2012 ◽  
Vol 20 (3) ◽  
pp. 5-20 ◽  
Author(s):  
İsmail Aydin
Keyword(s):  
Lebesgue Space ◽  
Variable Exponent ◽  
Weighted Lebesgue Space ◽  
Lebesgue Spaces ◽  
Wiener Amalgam Spaces ◽  
Local Component ◽  
Variable Exponent Lebesgue Space ◽  
New Family ◽  
Amalgam Spaces ◽  
Weighted Variable

Abstract We derive some of the basic properties of weighted variable exponent Lebesgue spaces Lp(.)w (ℝn) and investigate embeddings of these spaces under some conditions. Also a new family of Wiener amalgam spaces W(Lp(.)w ;Lqv) is defined, where the local component is a weighted variable exponent Lebesgue space Lp(.)w (ℝn) and the global component is a weighted Lebesgue space Lqv (ℝn) : We investigate the properties of the spaces W(Lp(.)w ;Lqv): We also present new Hölder-type inequalities and embeddings for these spaces.

scholarly journals On a measure of non-compactness for singular integrals

2003 ◽  
Vol 1 (1) ◽  
pp. 35-43 ◽  
Author(s):  
Alexander Meskhi
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Lebesgue Space ◽  
Singular Integrals ◽  
Weighted Lebesgue Space ◽  
Smooth Curves

It is proved that there exists no weight pair(v, w)for which a singular integral operator is compact from the weighted Lebesgue spaceLwp(Rn)toLvp(Rn). Moreover, a measure of non-compatness for this operator is estimated from below. Analogous problems for Cauchy singular integrals defined on Jordan smooth curves are studied.

Generalized Hankel operators on the Fock space

2009 ◽  
Vol 282 (12) ◽  
pp. 1811-1826 ◽  
Author(s):  
Georg Schneider ◽  
Kristan A. Schneider
Keyword(s):  
Fock Space ◽  
Hankel Operators
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