On the Boundedness of maximal and potential operators in variable exponent amalgam spaces

Abstract

Abstract. Two-weight estimates for maximal and fractional integral operators in variable exponent amalgam spaces (L p(·) ,l q ) are established under the log-Hölder continuity condition on the exponent p(·) . Some of the derived results are new even for constant p .Mathematics subject classification (2010): 42B25, 46E30.

Inverse continuous wavelet transform in weighted variable exponent amalgam spaces

“…In 2014, Meskhi and Zaighum showed that the maximal operator is bounded in weighted variable exponent amalgam spaces under some conditions [30].…”

“…Some interesting articles have been published on this subject, but not many. So there are many open problems in this function spaces [5], [21], [26], [30], [22], [28], [3], [7], [2], [6].…”

The Kolmogorov–Riesz theorem and some compactness criterions of bounded subsets in weighted variable exponent amalgam and Sobolev spaces

“…In 2014, Meskhi and Zaighum [27] proved the boundedness of maximal operator for weighted variable exponent amalgam spaces under some conditions, see [27,Theorem 3.3], [27,Theorem 3.4]. Throughout this paper, we assume that p (.)…”

“…Recently, there have been many interesting and important papers appeared in variable exponent amalgam spaces L r(.) , ℓ s such as Aydin [1], Aydin [3], Aydin and Gurkanli [4], Gurkanli [16], Gurkanli and Aydin [17], Hanche-Olsen and Holden [18], Meskhi and Zaighum [27], Kokilashvili, Meskhi and Zaighum [21] and Kulak and Gurkanli [24]. In 2003, Pandey studied the compactness of bounded subsets in a Wiener amalgam space W (B, Y ) whose local and global components are solid Banach function spaces and satisfy conditions in [29,Definition 5.1].…”

On vector-valued classical and variable exponent amalgam spaces

“…Comprehensive information about amalgam spaces can be found in some papers, such as [16], [29], [15], [10] and [11]. Recently, there have been many interesting and important papers appeared in variable exponent amalgam spaces L r(:) ;`s , such as Ayd¬n and Gürkanl¬ [3], Ayd¬n [5], Gürkanli and Ayd¬n [14], Kokilashvili, Meskhi and Zaighum [17], Meskhi and Zaighum [23], Gürkanli [13], Kulak and Gürkanli [20]. Vector-valued classical amalgam spaces (L p (R; E) ;`q) on the real line were de…ned by Lakshmi and Ray [21] in 2009.…”