id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6274	Sultan, Mehvish; Sultan, Babar; Popa, Ioan-Lucian	Grand Variable Herz-Morrey Type Besove Spaces and Triebel-Lizorkin Spaces	2025	33	.pdf	application/pdf	9801	598	88	If d > 0 and λ− d/2 < 0, then we get I4 ≲ sup ϵ>0 sup L⩽0,L∈Z 2−Lλ ϵθ L∑ k=−∞ ∞∑ i=L+3 2 dq(1+ϵ)(k−i) 2  i∑ m=−∞ 2η(0)mq(1+ϵ) ∥∥∥∥∥∥∥  ∞∑ j=1 |gj |r  1 r 1m ∥∥∥∥∥∥∥ q(1+ϵ) p(·)   1 q(1+ϵ) ≲ sup ϵ>0 sup L⩽0,L∈Z 2−Lλ { ϵθ L∑ k=−∞ ∞∑ i=L+3 2 dq(1+ϵ)(k−i) 2 · 2iq(1+ϵ)λE q(1+ϵ) f } 1 q(1+ϵ) M. Sultan, B. Sultan, I-L. Popa / Eur. Math, 18 (3) (2025), 6274 26 of 33 If l ∈ N, p0 = r ∈ (n/a,< min {p−, κ}) , N > max{0,−s}+a and ω := N+s−d/r > 0, then we get (∫ 2 1 ∣∣∣2ls (Φ∗ 2−lg ) a (x) ∣∣∣κ dt t )r/κ ≲ ∑ k∈l+N0 2−ωr|l−k|2krsM	cache/ejpam-6274.pdf	txt/ejpam-6274.txt