Bounded and Compact Integral Operators

One‐sided operators inLp(x)spaces

“…Motivation for the study of one-sided operators acting between classical Lebesgue spaces is provided in [30], [22], [11]. Our extension of this study to the setting of variable exponent spaces is not only natural but has the advantage that it shows that one-sided operators may be bounded under weaker conditions on the exponent than were known for two-sided operators.…”

Singular Integral Operators in Generalized Morrey Spaces on Curves in the Complex Plane

“…For Hardy-type operators in various function spaces, we refer for instance to [3,14], and the recent book [12], see also references therein. The boundedness of the operators (3.4) in generalized Morrey spaces was proved in [13].…”

Fractional and Hypersingular Operators in Variable Exponent Spaces on Metric Measure Spaces

“…From (2.4) we have 6) where c 1 > 0 does not depend on x ∈ Ω and r ∈ (0, diam(Ω)), and n need not to be an integer. We refer to [7], [8], [13], [18], [21], [26] for general properties of metric measure spaces.…”

“…the book [18] for I α , and the book [13] and papers [15], [16], [17] for I α n . In the next theorem, for functions on doubling measure spaces with upper bound (2.6), we deal with the "quasi-Sobolev" exponent q = q(n, N ) defined by 1…”