Бидний тухай
Багш ажилтан
The main goal of this paper is a study of a class of more accurate Hilbert-type inequalities involving partial sums. We first derive a discrete Hilbert-type inequality involving two partial sums and the kernel 1/ max(mλ, nλ). Then, by virtue of the Hardy inequality, we establish a weaker version of the latter relation involving only one partial sum, as well as the corresponding equivalent form. In addition, we prove that the constants appearing on the right-hand sides of the established inequalities are the best possible. Finally, we also give integral analogues of the corresponding discrete results.
In this paper, we establish a new Carlson type integral inequality with the best constant factor. The equivalent Beurling-Kjellberg type inequality and discrete form are considered.
Motivated by the results of Zhao and Cheung, we deduce a Hilbert-Pachpatte inequality with alternating signs involving non-homogeneous kernels. We also obtain a generalization of a related result known from the literature.
In this paper we establish necessary and sufficient conditions for the boundedness of a general Hilbert-type operator on the weighted Morrey-Herz spaces, without imposing conditions on a homogeneous kernel. As an application, some particular cases are also considered. Our results are compared with some previously known from the literature.
МУИС нь анхлан 1942 онд Мал эмнэлэг-зоотехник, Хүн эмнэлэг, Багш нарын факультет гэсэн гурван салбартайгаар хичээллэж эхлэхэд байгуулагдсан долоон тэнхимийн нэг нь Математикийн тэнхим юм. 1962 онд Математикийн тэнхим нь Математик анализын тэнихим, алгебрын тэнхим гэж хоёр тэнхим болж хуваагдсанаар Монгол улсад энэ салбар ухаанаар нэрлэгдсэн биеэ даасан нэгж бий болсон түүхтэй. Математик анализын тэнхим нь 2014 он хүртэл энэ нэрээ ямар нэг байдлаар хадгалсаар ирсэн байна. Энэхүү өгүүллээр МУИС-ийн математик анализын салбарын түүхэн хөгжил, бүрэлдэхүүн, сургалт, судалгааны голлох үр дүнгүүдийн тухай товч танилцуулсан болно.
Функцэн огторгуйн нэгэн сонирхолтой анги болох Херзийн огторгуйг Америкийн математикч Херз 1968 онд Фурье хувиргалтын абсолют нийлэлтийн тухай судалгааны ажилдаа анх танилцуулжээ. Энэ огторгуй дээр Гилбертийн оператор зааглагдах тухай үр дүнг 2009, 2012 онуудад ялгаатай нөхцөлтэй байдлаар Жичан нар тогтоосон. Хер- зийн огторгуйтай холбогддог өөр нэг сонирхолтой огторгуй нь Моррийн огторгуй юм. Эдгээр хоёр огторгуйн шууд өргөтгөл болдог огторгуйг Херз-Моррийн огторгуй гэдэг. Моррийн огторгуйд Гилбертийн оператор маш сайн судлагдсан байдаг. Иймд Гилбертийн операторын зааглалыг Херз-Моррийн огторгуйд тогтоох асуудал зүй ёсоор тавигдана. Энэхүү илтгэлийн хүрээнд дээрх асуудлын хариулт болох тогтоосон үр дүнгээ танилцуулах болно.
In this paper, we establish necessary and sufficient conditions for boundedness of m-linear p-adic integral operators with general homogeneous kernel on p-adic Lebesgue spaces and p-adic Morrey spaces, respectively. In each case, we obtain the corresponding operator norms. Also, we deal with some particular examples and compare them with the previously known from the literature.
In this paper, we establish necessary and sufficient conditions for boundedness of $m$- linear $p$-adic integral operators with general homogeneous kernel on $p$-adic Lebesgue spaces and $p$-adic Morrey spaces, respectively. In each case, we obtain the corresponding operator norms. Also, we deal with some particular examples and compare them with the previously known from the literature. This work was supported by National University of Mongolia, Project No. P2020-3990.
In the present study we provide a unified treatment of fractal Hilbert-type inequalities. Our main result is a pair of equivalent fractal Hilbert-type inequalities including a general kernel and weight functions. A particular emphasis is devoted to a class of homogeneous kernels. In addition, we impose appropriate conditions for which the constants appearing on the right-hand sides of the established inequalities are the best possible. As an application, our results are compared with some previously known from the literature.
In the present study we provide a unified treatment of fractal Hilbert-type inequalities. Our main result is a pair of equivalent fractal Hilbert-type inequalities including a general kernel and weight functions. A particular emphasis is devoted to a class of homogeneous kernels. In addition, we impose appropriate conditions for which the constants appearing on the right-hand sides of the established inequalities are the best possible. As an application, our results are compared with some previously known ones from the literature.
In the present paper we establish a unified treatment of Hilbert–Pachpatte-type inequalities for a class of non-homogeneous kernels. Our results are derived in both discrete and integral versions. A particular emphasis is devoted to constants and weight functions appearing on the right-hand sides of the established inequalities. As an application, we obtain inequalities with constants and weight functions expressed in terms of generalized harmonic numbers, the incomplete Beta and Gamma function, and the logarithmic integral function.
