On the Coefficient Multipliers of Bergman Spaces

Vukotić, Dragan

doi:10.1112/jlms/50.2.341

Cited by 17 publications

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“…We now compare our L ∞ -type necessary/sufficient multiplier estimates with the L q -type estimates for multipliers between unweighted Bergman spaces of [29]. Our sufficient conditions are easily seen to imply the following result.…”

Section: Sequential Estimates For Bergman Space Multipliersmentioning

confidence: 94%

“…Proposition 1 of [29] also gives a sufficient condition for each of four cases, but the powers of n in the sums are different and they change at p = 1 rather than p = 2 (see [29] for details). Naturally, one can also use the L q estimates of [29] to derive L ∞ estimates. Doing so, one sees that the two sets of results are incomparable if 0 < p 1, q > 0 and also if 1 < p < 2, q < p .…”

Section: Sequential Estimates For Bergman Space Multipliersmentioning

confidence: 99%

“…Since it is routine to derive such conditions from Theorems 4·7 and 4·8, we state a result only for the case where we get better estimates than those of the corresponding theorem 8 of [29]; we use 'O(N )' format for greater ease of comparability with theorem 8. Corollary 4·10 is stronger than Theorem 8 when q < min (2, p) and also when 1 < p < 2, q > p .…”

Section: Sequential Estimates For Bergman Space Multipliersmentioning

confidence: 99%

“…Blasco also described (A p , A 2 ) for 0 < p 1. Vukotić [29] had earlier characterized (A 1 , A 2 ) and had given several conditions which are either necessary or sufficient for membership of (A p , A q ) in certain cases such as 0 < p 2 q < ∞.…”

Section: Introductionmentioning

confidence: 99%

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Fractional integration, differentiation, and weighted Bergman spaces

Buckley

Koskela

Vukotić

1999

Math. Proc. Camb. Phil. Soc.

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Section: Sequential Estimates For Bergman Space Multipliersmentioning

confidence: 94%

Section: Sequential Estimates For Bergman Space Multipliersmentioning

confidence: 99%

Section: Sequential Estimates For Bergman Space Multipliersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fractional integration, differentiation, and weighted Bergman spaces

Buckley

Koskela

Vukotić

1999

Math. Proc. Camb. Phil. Soc.

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“…Recently the interest on similar questions has been renewed and some new results on multipliers on Hardy and Bergman spaces have been achieved (see [W,MP3,JP,MZ,V]). …”

Section: Introductionmentioning

confidence: 99%

Multipliers on Spaces of Analytic Functions

Blasco¹

1995

Can. j. math.

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Abstract. In the paper we find, for certain values of the parameters, the spaces of multipliers H (p, q, α), H(s, t, β) and H(p, q, α), l s , where H(p, q, α) denotes the space of analytic functions on the unit disc such thatAs corollaries we recover some new results about multipliers on Bergman spaces and Hardy spaces. §0.Introduction.Given two sequence spaces X and Y , we denote by (X, Y ) the space of multipliers from X into Y , that is the space of sequences of complex numbers (λ n ) such that (λ n a n ) ∈ Y for (a n ) ∈ X.When dealing with spaces of analytic functions defined on the open unit disc D we associate to each analytic function f (z) = ∞ n=0 a n z n the corresponding sequence of Taylor coefficients (a n ). In this sense any space of analytic functions is regarded as a sequence space and it makes sense to study multipliers acting on different classes of spaces such as Hardy spaces, Bergman spaces and so on. The aim of this paper is to study spaces of multipliers acting on certain general classes of analytic functions, denoted by H (p, q, α), which consists of functions on the unit disc such thatThe definition of these classes goes back to the work of Hardy and Littlewood (see [HL1,HL2]) and they were intensively studied for different reasons and by several authors. The reader is referred to the papers [DRS,F1,F2,MP1,S1,Sh] for information and properties on the spaces.There are two different techniques used in the paper. On one hand the use of a general theorem on operators acting on H(p, q, α) for 0 < p ≤ 1 which allows us to find H (p, q, α), H(s, t, β) and H(p, q, α), l s for the cases 0 < p, q ≤ 1 and 1 ≤ s, t ≤ ∞ and also for 0 < p ≤ 1 ≤ q although only for particular cases of s and t. In particular we can get a proof of the recent theorem, due to M. Mateljevic and 1991 Mathematics Subject Classification. 42A45.

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