scholarly journals Martingale Transforms between Martingale Hardy-amalgam Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Justice Sam Bansah
Keyword(s):  
Martingale Transforms ◽  
Amalgam Spaces

We discuss martingale transforms between martingale Hardy-amalgam spaces H p , q s , Q p , q and P p , q . Let 0 < p < q < ∞ , p 1 < p and q 1 < q and let f = f n , n ∈ ℕ be a martingale in P p 1 , q 1 ; then, we show that its martingale transforms are the martingales in P p , q for some p , q and similarly for H p , q s and Q p , q .

scholarly journals Hilbert space valued Gabor frames in weighted amalgam spaces

2019 ◽  
Vol 10 (4) ◽  
pp. 377-394
Author(s):  
Anirudha Poria ◽  
Jitendriya Swain
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Gabor Frame ◽  
Window Function ◽  
Gabor Frames ◽  
Frame Operator ◽  
Wiener Amalgam Space ◽  
Amalgam Spaces ◽  
Special Case

AbstractLet {\mathbb{H}} be a separable Hilbert space. In this paper, we establish a generalization of Walnut’s representation and Janssen’s representation of the {\mathbb{H}}-valued Gabor frame operator on {\mathbb{H}}-valued weighted amalgam spaces {W_{\mathbb{H}}(L^{p},L^{q}_{v})}, {1\leq p,q\leq\infty}. Also, we show that the frame operator is invertible on {W_{\mathbb{H}}(L^{p},L^{q}_{v})}, {1\leq p,q\leq\infty}, if the window function is in the Wiener amalgam space {W_{\mathbb{H}}(L^{\infty},L^{1}_{w})}. Further, we obtain the Walnut representation and invertibility of the frame operator corresponding to Gabor superframes and multi-window Gabor frames on {W_{\mathbb{H}}(L^{p},L^{q}_{v})}, {1\leq p,q\leq\infty}, as a special case by choosing the appropriate Hilbert space {\mathbb{H}}.

Martingale Transforms

2011 ◽  
pp. 97-107
Author(s):  
Burgess Davis ◽  
Renming Song
Keyword(s):  
Martingale Transforms

p-FRAMES FOR SUBSPACES OF WIENER AMALGAMS ON A LOCALLY COMPACT ABELIAN GROUP

2003 ◽  
Vol 01 (04) ◽  
pp. 481-489
Author(s):  
S. S. PANDEY
Keyword(s):  
Abelian Group ◽  
Compact Abelian Group ◽  
Closed Subspace ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Wiener Amalgam Spaces ◽  
Amalgam Spaces

We prove a theorem to characterize the p-frames for a shift invariant closed subspace of Wiener amalgam spaces [Formula: see text], 1 ≤ p ≤ q ≤ ∞, [Formula: see text] being a locally compact abelian group. Also, we show that a collection of translates under approximate conditions generaltes a p-frames for the space [Formula: see text].

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