scholarly journals The boundedness of commutators on locally compact Vilenkin groups

2005 ◽  
Vol 3 (2) ◽  
pp. 209-222
Author(s):  
Canqin Tang ◽  
Qingguo Li ◽  
Bolin Ma
Keyword(s):  
Integral Operator ◽  
Vilenkin Group ◽  
Locally Compact ◽  
Vilenkin Groups

LetGbe a locally compact Vilenkin group. In this paper, the authors investigate the boundedness of commutators of singluar integral operator on Triebel-Lizorkin spaces onG. Furthermore, the boundedness on the Herz-type Triebel-Lizorkin spaces are also studied.

scholarly journals The boundedness of multilinear commutators on locally compact Vilenkin groups

2006 ◽  
Vol 4 (3) ◽  
pp. 261-273 ◽  
Author(s):  
Canqin Tang
Keyword(s):  
Integral Operator ◽  
Hardy Spaces ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Vilenkin Group ◽  
Lebesgue Spaces ◽  
Locally Compact ◽  
Vilenkin Groups ◽  
Multilinear Commutators

LetGbe a locally compact Vilenkin group. In this paper, the authors investigate the boundedness of multilinear commutators of fractional integral operator on Lebesgue spaces onG. Furthermore, the boundedness on Hardy spaces are also obtained in this paper.

scholarly journals Lp-multipliers of mixed-norm type on locally compact Vilenkin groups

1998 ◽  
Vol 65 (3) ◽  
pp. 370-387 ◽  
Author(s):  
C. W. Onneweer ◽  
T. S. Quek
Keyword(s):  
Dual Group ◽  
Mixed Norm ◽  
Vilenkin Group ◽  
Locally Compact ◽  
Vilenkin Groups ◽  
Multiplier Theorems

AbstractLet G be a locally compact Vilenkin group with dual group Γ. We prove Littlewood-Paley type inequalities corresponding to arbitrary coset decompositions of Γ. These inequalities are then applied to obtain new Lp(G) multiplier theorems. The sharpness of some of these results is also discussed.

scholarly journals Multipliers for Hardy spaces on locally compact Vilenkin groups

1993 ◽  
Vol 55 (3) ◽  
pp. 287-301 ◽  
Author(s):  
C. W. Onneweer ◽  
T. S. Quek
Keyword(s):  
Hardy Spaces ◽  
Vilenkin Group ◽  
Multiplier Theorem ◽  
Herz Spaces ◽  
Locally Compact ◽  
Vilenkin Groups

AbstractIn a recent paper In a recent paper the authors proved a multiplier theorem for Hardy spaces Hp (G), 0 < p ≤ 1, defined on a locally compact Vilenkin group G. The assumptions on the multiplier were expressed in terms of the “norms” of certain Herz spaces K (1/p − 1/?r, r, p) with r restricted to 1 ≤ r < ∞ and p < r. In the present paper we show how this restriction on r may be weakened to p ≤ r ∞. Furthermore, we present two modifications of our main theorem and compare these with certain results for multipliers on LP (Rn)-spaces, 1 < p < ∞, due to Seeger and to Cowling, Fendler and Foumier. We also discuss the sharpness of some of our results.

scholarly journals Multipliers for weighted Hardy spaces on locally compact Vilenkin groups

1993 ◽  
Vol 48 (3) ◽  
pp. 441-449 ◽  
Author(s):  
Toshiyuki Kitada
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Vilenkin Group ◽  
Weighted Hardy Space ◽  
Weighted Hardy Spaces ◽  
Locally Compact ◽  
Vilenkin Groups ◽  
Hörmander Condition

Let G be a locally compact Vilenkin group. We study multipliers which satisfy a generalised Hörmander condition from power-weighted Hardy space (G) to (G) with 0 < p ≤ q < ∞, 0 < p ≤ 1, −1 < β, β′.

scholarly journals Potential operators and multipliers on locally compact Vilenkin groups

1996 ◽  
Vol 54 (3) ◽  
pp. 459-471 ◽  
Author(s):  
Toshiyuki Kitada
Keyword(s):  
Norm Inequality ◽  
Maximal Operators ◽  
Weighted Norm Inequality ◽  
Weighted Norm ◽  
Vilenkin Group ◽  
Locally Compact ◽  
Vilenkin Groups ◽  
Potential Operators ◽  
Fractional Type

We study, under the setting of a locally compact Vilenkin group G, a weighted norm inequality for the potential operators of Riesz type and its applications to multipliers on G. We also consider the maximal operators of fractional type.

scholarly journals N-Valid trees in wavelet theory on Vilenkin groups

2015 ◽  
Vol 13 (05) ◽  
pp. 1550037 ◽  
Author(s):  
S. F. Lukomskii ◽  
G. S. Berdnikov
Keyword(s):  
Rooted Tree ◽  
Step Function ◽  
Elementary Step ◽  
Vilenkin Group ◽  
Wavelet Theory ◽  
Vilenkin Groups ◽  
Step Functions

We consider a class of (N, M)-elementary step functions on the p-adic Vilenkin group. We prove that (N, M)-elementary step function generates a MRA on p-adic Vilenkin group if and only if it is generated by a special N-valid rooted tree on the set of vertices {0,1,…p - 1} with the vector (0,…,0) ∈ ℤN as a root.

WeightedH p multipliers on locally compact Vilenkin groups

1990 ◽  
Vol 110 (3-4) ◽  
pp. 283-295 ◽  
Author(s):  
Toshiyuki Kitada
Keyword(s):  
Locally Compact ◽  
Vilenkin Groups
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